SettingsNumerical analysis
Abramowitz and Stegun
Abramowitz and Stegun is the informal name of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the U.S. National Bureau of Standards (now the National Institut...
Abramowitz and Stegun is the informal name of a mathematical reference work edited by Milton Abramowitz and Irene Stegun of the U.S. National Bureau of Standards (now the National Institut...
Acoustic analogy
Acoustic analogies are applied mostly in numerical aeroacoustics to reduce aeroacoustic sound sources to simple emitter types.
Acoustic analogies are applied mostly in numerical aeroacoustics to reduce aeroacoustic sound sources to simple emitter types.
Adaptive stepsize
Adaptive stepsize is a technique in numerical analysis used for many problems, but mainly for integration.
Adaptive stepsize is a technique in numerical analysis used for many problems, but mainly for integration.
Adjoint state method
The adjoint state method is a numerical method for computing the gradient of a function or operator in a numerical optimization problem.
The adjoint state method is a numerical method for computing the gradient of a function or operator in a numerical optimization problem.
Affine arithmetic
Affine arithmetic (AA) is a model for self-validated numerical analysis.
Affine arithmetic (AA) is a model for self-validated numerical analysis.
Aitken's delta-squared process
In numerical analysis, Aitken's delta-squared process is a series acceleration method, used for accelerating the rate of convergence of a sequence.
In numerical analysis, Aitken's delta-squared process is a series acceleration method, used for accelerating the rate of convergence of a sequence.
Applied element method
The Applied Element Method (AEM) is a numerical analysis utilized in predicting the continuum and discrete behavior of structures.
The Applied Element Method (AEM) is a numerical analysis utilized in predicting the continuum and discrete behavior of structures.
Approximation
An approximation is a representation of something that is not exact, but still close enough to be useful.
An approximation is a representation of something that is not exact, but still close enough to be useful.
Approximation error
The approximation error in some data is the extrosion between an exact value and some approximation to it.
The approximation error in some data is the extrosion between an exact value and some approximation to it.
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.
Arithmetic precision
The precision of a value describes the number of digits that are used to express that value.
The precision of a value describes the number of digits that are used to express that value.
Autocorrelation technique
The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance.
The autocorrelation technique is a method for estimating the dominating frequency in a complex signal, as well as its variance.
Basis function
In mathematics, a basis function is an element of a particular basis for a function space.
In mathematics, a basis function is an element of a particular basis for a function space.
Bellman pseudospectral method
The Bellman pseudospectral method is a pseudospectral method for optimal control based on Bellman's principle of optimality.
The Bellman pseudospectral method is a pseudospectral method for optimal control based on Bellman's principle of optimality.
Bernstein polynomial
In the mathematical field of numerical analysis, a Bernstein polynomial, named after Sergei Natanovich Bernstein, is a polynomial in the Bernstein form, that is a linear combination of ...
In the mathematical field of numerical analysis, a Bernstein polynomial, named after Sergei Natanovich Bernstein, is a polynomial in the Bernstein form, that is a linear combination of ...
Bernstein's constant
Bernstein's constant, usually denoted by the Greek letter β, is a mathematical constant named after Sergei Natanovich Bernstein and is approximately equal to 0.2801694990.
Bernstein's constant, usually denoted by the Greek letter β, is a mathematical constant named after Sergei Natanovich Bernstein and is approximately equal to 0.2801694990.
Bi-directional delay line
In mathematics, a bi-directional delay line is a numerical analysis technique used in computer simulation for solving ordinary differential equations by converting them to hyperbolic equations.
In mathematics, a bi-directional delay line is a numerical analysis technique used in computer simulation for solving ordinary differential equations by converting them to hyperbolic equations.
Biology Monte Carlo method
Biology Monte Carlo methods (BioMOCA) have been developed at the University of Illinois at Urbana-Champaign to simulate ion transport in an electrolyte environment through ion channels or nano-p...
Biology Monte Carlo methods (BioMOCA) have been developed at the University of Illinois at Urbana-Champaign to simulate ion transport in an electrolyte environment through ion channels or nano-p...
BKM algorithm
The BKM algorithm is a shift-and-add algorithm for computing elementary functions, first published in 1994 by J.C. Bajard, S. Kla, and J.M. Muller.
The BKM algorithm is a shift-and-add algorithm for computing elementary functions, first published in 1994 by J.C. Bajard, S. Kla, and J.M. Muller.
Blossom (functional)
In numerical analysis, a blossom is a functional that can be applied to any polynomial, but is mostly used for Bézier and spline curves and surfaces.
In numerical analysis, a blossom is a functional that can be applied to any polynomial, but is mostly used for Bézier and spline curves and surfaces.
Boundary knot method
The boundary knot method (BKM) is proposed as an alternative boundary-type meshfree distance function collocation scheme.
The boundary knot method (BKM) is proposed as an alternative boundary-type meshfree distance function collocation scheme.
Boundary particle method
In applied mathematics, the boundary particle method is a truly boundary-only meshless collocation technique, in the sense that none of inner nodes are required at all in the numerical solution ...
In applied mathematics, the boundary particle method is a truly boundary-only meshless collocation technique, in the sense that none of inner nodes are required at all in the numerical solution ...
Butcher group
In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by, is an infinite-dimensional group first introduced in numerical analysis to study solutions of no...
In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by, is an infinite-dimensional group first introduced in numerical analysis to study solutions of no...
Cascade algorithm
In the mathematical topic of wavelet theory, the cascade algorithm is a numerical method for calculating function values of the basic scaling and wavelet functions of a discrete wavelet transfor...
In the mathematical topic of wavelet theory, the cascade algorithm is a numerical method for calculating function values of the basic scaling and wavelet functions of a discrete wavelet transfor...
Chebyshev nodes
In numerical analysis, Chebyshev nodes are the roots of the Chebyshev polynomial of the first kind.
In numerical analysis, Chebyshev nodes are the roots of the Chebyshev polynomial of the first kind.
Chebyshev polynomials
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.
In mathematics the Chebyshev polynomials, named after Pafnuty Chebyshev, are a sequence of orthogonal polynomials which are related to de Moivre's formula and which can be defined recursively.
Chebyshev pseudospectral method
The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind.
The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind.
Clenshaw algorithm
In numerical analysis, the Clenshaw algorithm is a recursive method to evaluate a linear combination of Chebyshev polynomials.
In numerical analysis, the Clenshaw algorithm is a recursive method to evaluate a linear combination of Chebyshev polynomials.
Complementarity theory
A complementarity problem is a type of mathematical optimization problem.
A complementarity problem is a type of mathematical optimization problem.
Complex wavelet transform
The complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT).
The complex wavelet transform (CWT) is a complex-valued extension to the standard discrete wavelet transform (DWT).
Computational electromagnetics
Computational electromagnetics, computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects a...
Computational electromagnetics, computational electrodynamics or electromagnetic modeling is the process of modeling the interaction of electromagnetic fields with physical objects a...
Computational magnetohydrodynamics
Computational magnetohydrodynamics (CMHD) is a rapidly developing branch of magnetohydrodynamics that uses numerical methods and algorithms to solve and analyze problems that involve electricall...
Computational magnetohydrodynamics (CMHD) is a rapidly developing branch of magnetohydrodynamics that uses numerical methods and algorithms to solve and analyze problems that involve electricall...
Computational statistics
Computational statistics, or statistical computing, is the interface between statistics and computer science.
Computational statistics, or statistical computing, is the interface between statistics and computer science.
Condition number
In the field of numerical analysis, the condition number of a function with respect to an argument measures the asymptotically worst case of how much the function can change in proportion to sm...
In the field of numerical analysis, the condition number of a function with respect to an argument measures the asymptotically worst case of how much the function can change in proportion to sm...
Constructions of low-discrepancy sequences
There are some standard constructions of low-discrepancy sequences.
There are some standard constructions of low-discrepancy sequences.
Continuous wavelet
In numerical analysis, continuous wavelets are functions used by the continuous wavelet transform.
In numerical analysis, continuous wavelets are functions used by the continuous wavelet transform.
CORDIC
CORDIC is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions.
CORDIC is a simple and efficient algorithm to calculate hyperbolic and trigonometric functions.
Curse of dimensionality
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing high-dimensional spaces that do not occur in low-dimensional settings such as the physical space ...
The curse of dimensionality refers to various phenomena that arise when analyzing and organizing high-dimensional spaces that do not occur in low-dimensional settings such as the physical space ...
Curve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.
De Boor's algorithm
In the mathematical subfield of numerical analysis the de Boor's algorithm is a fast and numerically stable algorithm for evaluating spline curves in B-spline form.
In the mathematical subfield of numerical analysis the de Boor's algorithm is a fast and numerically stable algorithm for evaluating spline curves in B-spline form.
De Casteljau's algorithm
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau.
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau.
Digital Library of Mathematical Functions
The Digital Library of Mathematical Functions is an online project at the National Institute of Standards and Technology to develop a major resource of mathematical reference data for special f...
The Digital Library of Mathematical Functions is an online project at the National Institute of Standards and Technology to develop a major resource of mathematical reference data for special f...
Discrete Fourier transform
In mathematics, the discrete Fourier transform is a specific kind of discrete transform, used in Fourier analysis.
In mathematics, the discrete Fourier transform is a specific kind of discrete transform, used in Fourier analysis.
Discrete wavelet transform
In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled.
In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled.
Discretization
In mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts.
In mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts.
Discretization error
In numerical analysis, computational physics, and simulation, discretization error is error resulting from the fact that a function of a continuous variable is represented in the computer by a f...
In numerical analysis, computational physics, and simulation, discretization error is error resulting from the fact that a function of a continuous variable is represented in the computer by a f...
Dynamic relaxation
Dynamic relaxation is a numerical method, which, among other things, can be used do "form-finding" for cable and fabric structures.
Dynamic relaxation is a numerical method, which, among other things, can be used do "form-finding" for cable and fabric structures.
Equioscillation theorem
The equioscillation theorem concerns the approximation of continuous functions using polynomials when the merit function is the maximum difference (Uniform norm).
The equioscillation theorem concerns the approximation of continuous functions using polynomials when the merit function is the maximum difference (Uniform norm).
Error analysis
Error analysis is the study of kind and quantity of error that occurs, particularly in the fields of applied mathematics, applied linguistics and statistics.
Error analysis is the study of kind and quantity of error that occurs, particularly in the fields of applied mathematics, applied linguistics and statistics.
Estrin's scheme
In numerical analysis Estrin's scheme, also known as Estrin's method, is an algorithm for numerical evaluation of polynomials.
In numerical analysis Estrin's scheme, also known as Estrin's method, is an algorithm for numerical evaluation of polynomials.
Euler calculus
Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions by integrating with respect to...
Euler calculus is a methodology from applied algebraic topology and integral geometry that integrates constructible functions and more recently definable functions by integrating with respect to...
Extreme Loading for Structures
Extreme Loading for Structures (ELS) - a commercial structural analysis software program based on the applied element method (AEM) for the automatic tracking and propagation of cracks, separatio...
Extreme Loading for Structures (ELS) - a commercial structural analysis software program based on the applied element method (AEM) for the automatic tracking and propagation of cracks, separatio...
False precision
False precision occurs when numerical data are presented in a manner that implies better precision than is actually the case; since precision is a limit to accuracy, this often leads to overconf...
False precision occurs when numerical data are presented in a manner that implies better precision than is actually the case; since precision is a limit to accuracy, this often leads to overconf...
Fast multipole method
The fast multipole method (FMM) is a mathematical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem.
The fast multipole method (FMM) is a mathematical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem.
FEE method
In mathematics, the method FEE is the method of fast summation of series of a special form.
In mathematics, the method FEE is the method of fast summation of series of a special form.
Finite pointset method
In applied mathematics, the Finite Pointset Method is a method for the solution of the equations governing viscous fluid flows, including the effects of heat and mass transfer.
In applied mathematics, the Finite Pointset Method is a method for the solution of the equations governing viscous fluid flows, including the effects of heat and mass transfer.
Finite volume method
The finite volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations LeVeque, 2002; Toro, 1999.
The finite volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations LeVeque, 2002; Toro, 1999.
Fixed point iteration
In numerical analysis, fixed point iteration is a method of computing fixed points of iterated functions.
In numerical analysis, fixed point iteration is a method of computing fixed points of iterated functions.
G space
G Space is a functional space used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings.
G Space is a functional space used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings.
Gal's accurate tables
Gal's accurate tables is a method devised by Shmuel Gal to provide accurate values of special functions using a lookup table and interpolation.
Gal's accurate tables is a method devised by Shmuel Gal to provide accurate values of special functions using a lookup table and interpolation.
Galerkin method
In mathematics, in the area of numerical analysis, Galerkin methods are a class of methods for converting a continuous operator problem (such as a differential equation) to a discrete problem.
In mathematics, in the area of numerical analysis, Galerkin methods are a class of methods for converting a continuous operator problem (such as a differential equation) to a discrete problem.
Generalized Gauss-Newton method
The generalized Gauss–Newton method is a generalization of the least-squares method originally described by Carl Friedrich Gauss and of Newton's method due to Isaac Newton to the case of constra...
The generalized Gauss–Newton method is a generalization of the least-squares method originally described by Carl Friedrich Gauss and of Newton's method due to Isaac Newton to the case of constra...
Generalized Gauss–Newton method
The generalized Gauss–Newton method is a generalization of the least-squares method originally described by Carl Friedrich Gauss and of Newton's method due to Isaac Newton to the case of constra...
The generalized Gauss–Newton method is a generalization of the least-squares method originally described by Carl Friedrich Gauss and of Newton's method due to Isaac Newton to the case of constra...
Guard digit
In numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error.
In numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error.
Hermes Project
Hermes (Higher-order modular finite element system) is a C++/Python library of algorithms for rapid development of adaptive hp-FEM solvers.
Hermes (Higher-order modular finite element system) is a C++/Python library of algorithms for rapid development of adaptive hp-FEM solvers.
Horner scheme
In numerical analysis, the Horner scheme, named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form.
In numerical analysis, the Horner scheme, named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form.
Horner's method
In numerical analysis, the Horner scheme (also known as Horner algorithm), named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form.
In numerical analysis, the Horner scheme (also known as Horner algorithm), named after William George Horner, is an algorithm for the efficient evaluation of polynomials in monomial form.
Hundred-dollar, Hundred-digit Challenge problems
The Hundred-dollar, Hundred-digit Challenge problems are 10 problems in numerical mathematics published in 2002 by.
The Hundred-dollar, Hundred-digit Challenge problems are 10 problems in numerical mathematics published in 2002 by.
Hypot
Hypot is a mathematical function defined to calculate the length of the hypotenuse of a right-angle triangle.
Hypot is a mathematical function defined to calculate the length of the hypotenuse of a right-angle triangle.
Image-based meshing
Image-based meshing is the automated process of creating computer models for computational fluid dynamics and finite element analysis from 3D image data.
Image-based meshing is the automated process of creating computer models for computational fluid dynamics and finite element analysis from 3D image data.
International Workshops on Lattice QCD and Numerical Analysis
The International Workshops on Lattice QCD and Numerical Analysis first started in 1995.
The International Workshops on Lattice QCD and Numerical Analysis first started in 1995.
Interval arithmetic
Interval arithmetic, interval mathematics, interval analysis, or interval computation, is a method developed by mathematicians since the 1950s and 1960s as an approach to putti...
Interval arithmetic, interval mathematics, interval analysis, or interval computation, is a method developed by mathematicians since the 1950s and 1960s as an approach to putti...
Iterative method
In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems.
In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems.
Jenkins-Traub algorithm
The Jenkins-Traub algorithm for polynomial zeros is a fast globally convergent iterative method.
The Jenkins-Traub algorithm for polynomial zeros is a fast globally convergent iterative method.
Kahan summation algorithm
In numerical analysis, the Kahan summation algorithm (also known as compensated summation) significantly reduces the numerical error in the total obtained by adding a sequence of finite pr...
In numerical analysis, the Kahan summation algorithm (also known as compensated summation) significantly reduces the numerical error in the total obtained by adding a sequence of finite pr...
Kempner series
The Kempner series is a modification of the harmonic series, formed by omitting all terms whose denominator expressed in base 10 contains a 9 digit.
The Kempner series is a modification of the harmonic series, formed by omitting all terms whose denominator expressed in base 10 contains a 9 digit.
Lady Windermere's Fan (mathematics)
In mathematics, Lady Windermere's Fan is a telescopic identity employed to relate global and local error of a numerical algorithm.
In mathematics, Lady Windermere's Fan is a telescopic identity employed to relate global and local error of a numerical algorithm.
Lanczos approximation
In mathematics, the Lanczos approximation is a method for computing the Gamma function numerically, published by Cornelius Lanczos in 1964.
In mathematics, the Lanczos approximation is a method for computing the Gamma function numerically, published by Cornelius Lanczos in 1964.
Legendre pseudospectral method
The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials.
The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials.
Level set method
The level set method (sometimes abbreviated as LSM) is a numerical technique for tracking interfaces and shapes.
The level set method (sometimes abbreviated as LSM) is a numerical technique for tracking interfaces and shapes.
Levinson recursion
Levinson recursion or Levinson-Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix.
Levinson recursion or Levinson-Durbin recursion is a procedure in linear algebra to recursively calculate the solution to an equation involving a Toeplitz matrix.
Linear approximation
In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function).
In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function).
Loss of significance
Loss of significance is an undesirable effect in calculations using floating-point arithmetic.
Loss of significance is an undesirable effect in calculations using floating-point arithmetic.
Low-discrepancy sequence
In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x1, ..., xN has a low discrepancy.
In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x1, ..., xN has a low discrepancy.
Mesh generation
Mesh generation is the practice of generating a polygonal or polyhedral mesh that approximates a geometric domain.
Mesh generation is the practice of generating a polygonal or polyhedral mesh that approximates a geometric domain.
Meshfree methods
Meshfree methods are a particular class of numerical simulation algorithms for the simulation of physical phenomena.
Meshfree methods are a particular class of numerical simulation algorithms for the simulation of physical phenomena.
Method of fundamental solution
The method of fundamental solution (MFS) is getting a growing attention in scientific computation and simulation community.
The method of fundamental solution (MFS) is getting a growing attention in scientific computation and simulation community.
Method of fundamental solutions
The method of fundamental solutions is getting a growing attention in scientific computation and simulation community.
The method of fundamental solutions is getting a growing attention in scientific computation and simulation community.
Minimax approximation algorithm
Algorithms that minimize the maximum error are known as Minimax approximation algorithms.
Algorithms that minimize the maximum error are known as Minimax approximation algorithms.
Minimum polynomial extrapolation
In mathematics, minimum polynomial extrapolation is a sequence transformation used for convergence acceleration.
In mathematics, minimum polynomial extrapolation is a sequence transformation used for convergence acceleration.
Monte Carlo method
Monte Carlo methods (or Monte Carlo experiments) are a class of computational algorithms that rely on repeated random sampling to compute their results.
Monte Carlo methods (or Monte Carlo experiments) are a class of computational algorithms that rely on repeated random sampling to compute their results.
Morris Method
The Morris method for global sensitivity analysis is a so-called one step-at-a-time method, meaning that in each run only one input parameter is given a new value.
The Morris method for global sensitivity analysis is a so-called one step-at-a-time method, meaning that in each run only one input parameter is given a new value.
Morris method
In applied statistics, the Morris method for global sensitivity analysis is a so-called one step-at-a-time method, meaning that in each run only one input parameter is given a new value.
In applied statistics, the Morris method for global sensitivity analysis is a so-called one step-at-a-time method, meaning that in each run only one input parameter is given a new value.
Movable cellular automaton
The Movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept.
The Movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept.
Multigrid method
Multigrid (MG) methods in numerical analysis are a group of algorithms for solving differential equations using a hierarchy of discretizations.
Multigrid (MG) methods in numerical analysis are a group of algorithms for solving differential equations using a hierarchy of discretizations.
Multiphysics
Multiphysics treats simulations that involve multiple physical models or multiple simultaneous physical phenomena.
Multiphysics treats simulations that involve multiple physical models or multiple simultaneous physical phenomena.
Multiphysics Methods Group
The Multiphysics Methods Group (MMG) is a program at Idaho National Laboratory (under the U.S. Department of Energy) begun in 2004.
The Multiphysics Methods Group (MMG) is a program at Idaho National Laboratory (under the U.S. Department of Energy) begun in 2004.
NCLab
NCLab (Networked Computing Laboratory), freely accessible at is an interactive web framework for computer programming, computer modeling, and scientific computing.
NCLab (Networked Computing Laboratory), freely accessible at is an interactive web framework for computer programming, computer modeling, and scientific computing.
Nearest neighbor search
Nearest neighbor search (NNS), also known as proximity search, similarity search or closest point search, is an optimization problem for finding closest points in metric ...
Nearest neighbor search (NNS), also known as proximity search, similarity search or closest point search, is an optimization problem for finding closest points in metric ...
Non-linear least squares
Non-linear least squares is the form of least squares analysis which is used to fit a set of m observations with a model that is non-linear in n unknown parameters.
Non-linear least squares is the form of least squares analysis which is used to fit a set of m observations with a model that is non-linear in n unknown parameters.
Nonstandard finite difference scheme
Nonstandard finite difference schemes is a general set of methods in numerical analysis that gives numerical solutions to differential equations by constructing a discrete model.
Nonstandard finite difference schemes is a general set of methods in numerical analysis that gives numerical solutions to differential equations by constructing a discrete model.
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from dis...
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from dis...
Numerical differentiation
In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps oth...
In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps oth...
Numerical error
In software engineering and mathematics, numerical error is the combined effect of two kinds of error in a calculation.
In software engineering and mathematics, numerical error is the combined effect of two kinds of error in a calculation.
Numerical integration
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral and by extension, the term is also sometimes used...
In numerical analysis, numerical integration constitutes a broad family of algorithms for calculating the numerical value of a definite integral and by extension, the term is also sometimes used...
Numerical model of solar system
A numerical model of the solar system is a set of mathematical equations, which, when solved, give the approximate positions of the planets as a function of time.
A numerical model of the solar system is a set of mathematical equations, which, when solved, give the approximate positions of the planets as a function of time.
Numerical model of the Solar System
A numerical model of the Solar System is a set of mathematical equations, which, when solved, give the approximate positions of the planets as a function of time.
A numerical model of the Solar System is a set of mathematical equations, which, when solved, give the approximate positions of the planets as a function of time.
Numerical stability
In the mathematical subfield of numerical analysis, numerical stability is a desirable property of numerical algorithms.
In the mathematical subfield of numerical analysis, numerical stability is a desirable property of numerical algorithms.
Orders of approximation
In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more ref...
In science, engineering, and other quantitative disciplines, orders of approximation refer to formal or informal terms for how precise an approximation is, and to indicate progressively more ref...
Padé approximant
Padé approximant is the "best" approximation of a function by a rational function of given order - under this technique, the approximant's power series agrees with the power series of the functi...
Padé approximant is the "best" approximation of a function by a rational function of given order - under this technique, the approximant's power series agrees with the power series of the functi...
Padé table
In complex analysis, a Padé table is an array, possibly of infinite extent, of the rational Padé approximants :Rm, n to a given complex formal power series.
In complex analysis, a Padé table is an array, possibly of infinite extent, of the rational Padé approximants :Rm, n to a given complex formal power series.
Pairwise summation
In numerical analysis, pairwise summation, also called cascade summation, is a technique to sum a sequence of finite-precision floating-point numbers that substantially reduces the accumul...
In numerical analysis, pairwise summation, also called cascade summation, is a technique to sum a sequence of finite-precision floating-point numbers that substantially reduces the accumul...
Piecewise linear continuation
Piecewise linear continuation is similar to contour plotting (Dobkin, Silvio, Thurston and Wilks 5), but in higher dimensions.
Piecewise linear continuation is similar to contour plotting (Dobkin, Silvio, Thurston and Wilks 5), but in higher dimensions.
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multip...
In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multip...
Predictor-corrector method
In mathematics, particularly numerical analysis, a predictor–corrector method is an algorithm that proceeds in two steps.
In mathematics, particularly numerical analysis, a predictor–corrector method is an algorithm that proceeds in two steps.
Propagation of uncertainty
In statistics, propagation of uncertainty is the effect of variables' uncertainties on the uncertainty of a function based on them.
In statistics, propagation of uncertainty is the effect of variables' uncertainties on the uncertainty of a function based on them.
Pseudo-spectral method
Pseudo-spectral methods are a class of numerical methods used in applied mathematics and scientific computing for the solution of PDEs, such as the direct simulation of a particle with an arbi...
Pseudo-spectral methods are a class of numerical methods used in applied mathematics and scientific computing for the solution of PDEs, such as the direct simulation of a particle with an arbi...
Pseudospectral knotting method
The Pseudospectral knotting method is a generalization and enhancement of a standard pseudospectral method for optimal control.
The Pseudospectral knotting method is a generalization and enhancement of a standard pseudospectral method for optimal control.
Rate of convergence
In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.
In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.
Regularized meshless method
In numerical mathematics, the regularized meshless method, also known as the singular meshless method or desingularized meshless method, is a meshless boundary collocation method des...
In numerical mathematics, the regularized meshless method, also known as the singular meshless method or desingularized meshless method, is a meshless boundary collocation method des...
Relative change and difference
The relative difference, percent difference, relative percent difference, or percentage difference between two quantities is the difference between them, expressed as a compari...
The relative difference, percent difference, relative percent difference, or percentage difference between two quantities is the difference between them, expressed as a compari...
Remez algorithm
The Remez algorithm, published by Evgeny Yakovlevich Remez in 1934 is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in the Che...
The Remez algorithm, published by Evgeny Yakovlevich Remez in 1934 is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in the Che...
Residual (numerical analysis)
Loosely speaking, a residual is the error in a result.
Loosely speaking, a residual is the error in a result.
Richardson extrapolation
In numerical analysis, Richardson extrapolation is a sequence acceleration method, used to improve the rate of convergence of a sequence.
In numerical analysis, Richardson extrapolation is a sequence acceleration method, used to improve the rate of convergence of a sequence.
Riemann solver
A Riemann solver is a numerical method used to solve a Riemann problem.
A Riemann solver is a numerical method used to solve a Riemann problem.
Ross-Fahroo lemma
The Ross–Fahroo lemma is a fundamental result in optimal control theory.
The Ross–Fahroo lemma is a fundamental result in optimal control theory.
Ross-Fahroo pseudospectral method
The Ross–Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control introduced by Ross and Fahroo, at the turn of the millennium.
The Ross–Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control introduced by Ross and Fahroo, at the turn of the millennium.
Ross-Fahroo Pseudospectral Methods
The Ross-Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control introduced by Ross and Fahroo, at the turn of the millennium.
The Ross-Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control introduced by Ross and Fahroo, at the turn of the millennium.
Round-off error
A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value.
A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value.
ScanIP
ScanIP is an image processing software package developed by Simpleware Ltd. ScanIP visualises and segments 3D image data from MRI, CT, or Microtomography).
ScanIP is an image processing software package developed by Simpleware Ltd. ScanIP visualises and segments 3D image data from MRI, CT, or Microtomography).
Semi-infinite programming
In optimization theory, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variabl...
In optimization theory, semi-infinite programming (SIP) is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variabl...
Series acceleration
In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series.
In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series.
Shanks transformation
In numerical analysis, the Shanks transformation is a non-linear series acceleration method to increase the rate of convergence of a sequence.
In numerical analysis, the Shanks transformation is a non-linear series acceleration method to increase the rate of convergence of a sequence.
Sigma approximation
In mathematics, σ-approximation adjusts a Fourier summation to eliminate the Gibbs phenomenon which would otherwise occur at discontinuities.
In mathematics, σ-approximation adjusts a Fourier summation to eliminate the Gibbs phenomenon which would otherwise occur at discontinuities.
Significance arithmetic
Significance arithmetic is a set of rules (sometimes called significant figure rules) for approximating the propagation of uncertainty in scientific or statistical calculations.
Significance arithmetic is a set of rules (sometimes called significant figure rules) for approximating the propagation of uncertainty in scientific or statistical calculations.
Simpson's rule
In numerical analysis, Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals.
In numerical analysis, Simpson's rule is a method for numerical integration, the numerical approximation of definite integrals.
Sinc numerical methods
In numerical analysis and applied mathematics, sinc numerical methods are numerical techniques for finding approximate solutions of partial differential equations and integral equations based on...
In numerical analysis and applied mathematics, sinc numerical methods are numerical techniques for finding approximate solutions of partial differential equations and integral equations based on...
Smoothed finite element method
Smoothed Finite Element methods are a particular class of numerical simulation algorithms for the simulation of physical phenomena.
Smoothed Finite Element methods are a particular class of numerical simulation algorithms for the simulation of physical phenomena.
Sparse grid
Sparse grids are a numerical technique to represent, integrate or interpolate high dimensional functions.
Sparse grids are a numerical technique to represent, integrate or interpolate high dimensional functions.
Spectral method
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, often involving the use of the Fast Fourier T...
Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations, often involving the use of the Fast Fourier T...
Successive parabolic interpolation
Successive parabolic interpolation is a technique for finding the extremum (minimum or maximum) of a continuous unimodal function by successively fitting parabolas (polynomials of degree two) to...
Successive parabolic interpolation is a technique for finding the extremum (minimum or maximum) of a continuous unimodal function by successively fitting parabolas (polynomials of degree two) to...
Superconvergence
In numerical analysis, a superconvergent method is one which converges faster than generally expected.
In numerical analysis, a superconvergent method is one which converges faster than generally expected.
Surrogate model
One way of alleviating this burden is by constructing approximation models, known as surrogate models, response surface models, metamodels or emulators, that mimic the behavior of the simulation...
One way of alleviating this burden is by constructing approximation models, known as surrogate models, response surface models, metamodels or emulators, that mimic the behavior of the simulation...
Symbolic-numeric computation
In mathematics and computer science, symbolic-numeric computation is the use of software that combines symbolic and numeric methods to solve problems.
In mathematics and computer science, symbolic-numeric computation is the use of software that combines symbolic and numeric methods to solve problems.
Trajectory (fluid mechanics)
In fluid mechanics, meteorology and oceanography, a trajectory traces the motion of a single point, often called a parcel, in the flow.
In fluid mechanics, meteorology and oceanography, a trajectory traces the motion of a single point, often called a parcel, in the flow.
Transfer matrix
The transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions.
The transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions.
Trigonometric tables
Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineering.
Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineering.
Truncated power function
In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition.
In the mathematical subfield of numerical analysis, a B-spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition.
Truncation
In mathematics and computer science, truncation is the term for limiting the number of digits right of the decimal point, by discarding the least significant ones.
In mathematics and computer science, truncation is the term for limiting the number of digits right of the decimal point, by discarding the least significant ones.
Truncation error
Truncation error or local truncation error is error made by numerical algorithms that arises from taking finite number of steps in computation.
Truncation error or local truncation error is error made by numerical algorithms that arises from taking finite number of steps in computation.
Vector field reconstruction
Vector field reconstruction is a method of creating a vector field from experimental or computer generated data, usually with the goal of finding a differential equation model of the system.
Vector field reconstruction is a method of creating a vector field from experimental or computer generated data, usually with the goal of finding a differential equation model of the system.
Verified computing
In computer science, verified computing is a strategy and collection of techniques to ensure that calculations implemented in computer software yield results whose numerical precision can be gu...
In computer science, verified computing is a strategy and collection of techniques to ensure that calculations implemented in computer software yield results whose numerical precision can be gu...
Von Neumann stability analysis
In numerical analysis, von Neumann stability analysis (also known as Fourier stability analysis) is a procedure used to check the stability of finite difference schemes as applied to linear part...
In numerical analysis, von Neumann stability analysis (also known as Fourier stability analysis) is a procedure used to check the stability of finite difference schemes as applied to linear part...
Weakened weak form
Weakened weak form (or W2 form) is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings.
Weakened weak form (or W2 form) is used in the formulation of general numerical methods based on meshfree methods and/or finite element method settings.
Well-posed problem
The mathematical term well-posed problem stems from a definition given by Jacques Hadamard.
The mathematical term well-posed problem stems from a definition given by Jacques Hadamard.
Wilkinson's polynomial
In numerical analysis, Wilkinson's polynomial is a specific polynomial which was used by James H. Wilkinson in 1963 to illustrate a difficulty when finding the root of a polynomial: the location...
In numerical analysis, Wilkinson's polynomial is a specific polynomial which was used by James H. Wilkinson in 1963 to illustrate a difficulty when finding the root of a polynomial: the location...