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Coordinate Rotation Digital Computer

No description available.

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. These numerical methods are applicable to solid

Multigrid method

In numerical analysis, a multigrid method (MG method) is an algorithm for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multi

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 of th

Local linearization method

In numerical analysis, the local linearization (LL) method is a general strategy for designing numerical integrators for differential equations based on a local (piecewise) linearization of the given

Numerical error

In software engineering and mathematics, numerical error is the error in the numerical computations.

Numerical methods in fluid mechanics

Fluid motion is governed by the Navier–Stokes equations, a set of coupled and nonlinearpartial differential equations derived from the basic laws of conservation of mass, momentumand energy. The unkno

Order of approximation

In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is.

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 constrained n

NIST Handbook of Mathematical Functions

No description available.

Unisolvent functions

In mathematics, a set of n functions f1, f2, ..., fn is unisolvent (meaning "uniquely solvable") on a domain Ω if the vectors are linearly independent for any choice of n distinct points x1, x2 ... xn

Hundred-dollar, Hundred-digit Challenge problems

The Hundred-dollar, Hundred-digit Challenge problems are 10 problems in numerical mathematics published in 2002 by Nick Trefethen. A $100 prize was offered to whoever produced the most accurate soluti

De Boor's algorithm

In the mathematical subfield of numerical analysis de Boor's algorithm is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de

Multilevel Monte Carlo method

Multilevel Monte Carlo (MLMC) methods in numerical analysis are algorithms for computing expectations that arise in stochastic simulations. Just as Monte Carlo methods, they rely on repeated random sa

Closest point method

The closest point method (CPM) is an embedding method for solving partial differential equations on surfaces. The closest point method uses standard numerical approaches such as finite differences, fi

Generalized-strain mesh-free formulation

The generalized-strain mesh-free (GSMF) formulation is a local meshfree method in the field of numerical analysis, completely integration free, working as a weighted-residual weak-form collocation. Th

Regge calculus

In general relativity, Regge calculus is a formalism for producing simplicial approximations of spacetimes that are solutions to the Einstein field equation. The calculus was introduced by the Italian

Discrete Fourier transform

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fouri

Butcher group

In mathematics, the Butcher group, named after the New Zealand mathematician John C. Butcher by , is an infinite-dimensional Lie group first introduced in numerical analysis to study solutions of non-

Curse of dimensionality

The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensi

Stiffness matrix

In the finite element method for the numerical solution of elliptic partial differential equations, the stiffness matrix is a matrix that represents the system of linear equations that must be solved

Factor combining

No description available.

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. A differe

Radial basis function

A radial basis function (RBF) is a real-valued function whose value depends only on the distance between the input and some fixed point, either the origin, so that , or some other fixed point , called

Newton–Krylov method

Newton–Krylov methods are numerical methods for solving non-linear problems using Krylov subspace linear solvers. The Newton method, when generalised to systems of multiple variables, includes the inv

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 partial di

Condition number

In numerical analysis, the condition number of a function measures how much the output value of the function can change for a small change in the input argument. This is used to measure how sensitive

Aitken's delta-squared process

In numerical analysis, Aitken's delta-squared process or Aitken extrapolation is a series acceleration method, used for accelerating the rate of convergence of a sequence. It is named after Alexander

Simpson's rule

In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761). The most basic of these rules, called Simpson's 1/3 rule, or just S

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is nu

Approximation

An approximation is anything that is intentionally similar but not exactly equal to something else.

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. As with other wavelet transforms, a key advant

GetFEM++

GetFEM++ is a generic finite element C++ library with interfaces for Python, Matlab and Scilab. It aims at providing finite element methods and elementary matrix computations for solving linear and no

Composite methods for structural dynamics

Composite methods are an approach applied in structural dynamics and related fields. They combine various methods in each time step, in order to acquire the advantages of different methods. The existi

Multiphysics simulation

In computational modelling, multiphysics simulation (often shortened to simply "multiphysics") is defined as the simultaneous simulation of different aspects of a physical system or systems and the in

Newton fractal

The Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial p(Z) ∈ ℂ[Z] or transcendental function. It is the Julia set of the mer

Mesh generation

Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells.Often these cells form a simplicial complex.Usually the

Richardson extrapolation

In numerical analysis, Richardson extrapolation is a sequence acceleration method used to improve the rate of convergence of a sequence of estimates of some value . In essence, given the value of for

Uzawa iteration

In numerical mathematics, the Uzawa iteration is an algorithm for solving saddle point problems. It is named after Hirofumi Uzawa and was originally introduced in the context of concave programming.

Remez algorithm

The Remez algorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations

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 the t

Meshfree methods

In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with

Discretization

In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first

Artificial precision

In numerical mathematics, artificial precision is a source of error that occurs when a numerical value or semantic is expressed with more precision than was initially provided from measurement or user

Overlap–add method

In signal processing, the overlap–add method is an efficient way to evaluate the discrete convolution of a very long signal with a finite impulse response (FIR) filter : where h[m] = 0 for m outside t

Nyström method

In mathematics numerical analysis, the Nyström method or quadrature method seeks the numerical solution of an integral equation by replacing the integral with a representative weighted sum. The contin

Estrin's scheme

In numerical analysis, Estrin's scheme (after Gerald Estrin), also known as Estrin's method, is an algorithm for numerical evaluation of polynomials. Horner's method for evaluation of polynomials is o

Van Wijngaarden transformation

In mathematics and numerical analysis, the van Wijngaarden transformation is a variant on the Euler transform used to accelerate the convergence of an alternating series. One algorithm to compute Eule

Partial differential algebraic equation

In mathematics a partial differential algebraic equation (PDAE) set is an incomplete system of partial differential equations that is closed with a set of algebraic equations.

Piecewise linear continuation

Simplicial continuation, or piecewise linear continuation (Allgower and Georg), is a one-parameter continuation method which is well suited to small to medium embedding spaces. The algorithm has been

INTLAB

INTLAB (INTerval LABoratory) is an interval arithmetic library using MATLAB and GNU Octave, available in Windows and Linux, macOS. It was developed by S.M. Rump from Hamburg University of Technology.

Runge–Kutta–Fehlberg method

In mathematics, the Runge–Kutta–Fehlberg method (or Fehlberg method) is an algorithm in numerical analysis for the numerical solution of ordinary differential equations. It was developed by the German

Padé approximant

In mathematics, a Padé approximant is the "best" approximation of a function near a specific point by a rational function of given order. Under this technique, the approximant's power series agrees wi

Differential CORDIC

No description available.

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 thi

Merged CORDIC

No description available.

Truncation

In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.

Iterative rational Krylov algorithm

The iterative rational Krylov algorithm (IRKA), is an iterative algorithm, useful for model order reduction (MOR) of single-input single-output (SISO) linear time-invariant dynamical systems. At each

Affine arithmetic

Affine arithmetic (AA) is a model for self-validated numerical analysis. In AA, the quantities of interest are represented as affine combinations (affine forms) of certain primitive variables, which s

Unrestricted algorithm

An unrestricted algorithm is an algorithm for the computation of a mathematical function that puts no restrictions on the range of the argument or on the precision that may be demanded in the result.

Anderson acceleration

In mathematics, Anderson acceleration, also called Anderson mixing, is a method for the acceleration of the convergence rate of fixed-point iterations. Introduced by Donald G. Anderson, this technique

Scarborough criterion

The Scarborough criterion is used for satisfying convergence of a solution while solving linear equations using an iterative method.

Peano kernel theorem

In numerical analysis, the Peano kernel theorem is a general result on error bounds for a wide class of numerical approximations (such as numerical quadratures), defined in terms of linear functionals

Guard digit

In numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error. For example, suppose that the final result of a long, multi-step calculation can be safely rounded o

Monte Carlo method

Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use rando

FEE method

In mathematics, the FEE method, or fast E-function evaluation method, is the method of fast summation of series of a special form. It was constructed in 1990 by and is so-named because it makes fast c

Legendre pseudospectral method

The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. A basic vers

List of uncertainty propagation software

List of uncertainty propagation software used to perform propagation of uncertainty calculations:

Difference quotient

In single-variable calculus, the difference quotient is usually the name for the expression which when taken to the limit as h approaches 0 gives the derivative of the function f. The name of the expr

Well-posed problem

The mathematical term well-posed problem stems from a definition given by 20th-century French mathematician Jacques Hadamard. He believed that mathematical models of physical phenomena should have the

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. Attempts to create such a model estab

Numerical differentiation

In numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the

Horner's method

In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has be

Transfer matrix

In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions. Refinable functions play an importa

Cell-based models

Cell-based models are mathematical models that represent biological cells as a discrete entities. Within the field of computational biology they are often simply called agent-based models of which the

Hermes Project

Hermes2D (Higher-order modular finite element system) is a C++/Python library of algorithms for rapid development of adaptive hp-FEM solvers. hp-FEM is a modern version of the finite element method (F

Redundant CORDIC

No description available.

Bernstein polynomial

In the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial that is a linear combination of Bernstein basis polynomials. The idea is named after Sergei Natanovich Bernstein

Applied element method

The applied element method (AEM) is a numerical analysis used in predicting the continuum and discrete behavior of structures. The modeling method in AEM adopts the concept of discrete cracking allowi

Minimum polynomial extrapolation

In mathematics, minimum polynomial extrapolation is a sequence transformation used for convergence acceleration of vector sequences, due to Cabay and Jackson. While Aitken's method is the most famous,

CORDIC

CORDIC (for "coordinate rotation digital computer"), also known as Volder's algorithm, or: Digit-by-digit method Circular CORDIC (Jack E. Volder), Linear CORDIC, Hyperbolic CORDIC (John Stephen Walthe

Exponential integrator

Exponential integrators are a class of numerical methods for the solution of ordinary differential equations, specifically initial value problems. This large class of methods from numerical analysis i

Adaptive step size

In mathematics and numerical analysis, an adaptive step size is used in some methods for the numerical solution of ordinary differential equations (including the special case of numerical integration)

Approximation error

The approximation error in a data value is the discrepancy between an exact value and some approximation to it. This error can be expressed as an absolute error (the numerical amount of the discrepanc

Numeric precision in Microsoft Excel

As with other spreadsheets, Microsoft Excel works only to limited accuracy because it retains only a certain number of figures to describe numbers (it has limited precision). With some exceptions rega

Order of accuracy

In numerical analysis, order of accuracy quantifies the rate of convergence of a numerical approximation of a differential equation to the exact solution.Consider , the exact solution to a differentia

Identifiability analysis

Identifiability analysis is a group of methods found in mathematical statistics that are used to determine how well the parameters of a model are estimated by the quantity and quality of experimental

Bellman pseudospectral method

The Bellman pseudospectral method is a pseudospectral method for optimal control based on Bellman's principle of optimality. It is part of the larger theory of pseudospectral optimal control, a term c

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the

List of finite element software packages

This is a list of notable software packages that implement the finite element method for solving partial differential equations.

Comparison of linear algebra libraries

The following tables provide a comparison of linear algebra software libraries, either specialized or general purpose libraries with significant linear algebra coverage.

Equioscillation theorem

In mathematics, the equioscillation theorem concerns the approximation of continuous functions using polynomials when the merit function is the maximum difference (uniform norm). Its discovery is attr

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. Certain sequences of approximants lying with

Ross–Fahroo lemma

Named after I. Michael Ross and F. Fahroo, the Ross–Fahroo lemma is a fundamental result in optimal control theory. It states that dualization and discretization are, in general, non-commutative opera

Pipelined CORDIC

No description available.

Principles of grid generation

No description available.

Method of fundamental solutions

In scientific computation and simulation, the method of fundamental solutions (MFS) is a technique for solving partial differential equations based on using the fundamental solution as a basis functio

Sigma approximation

In mathematics, σ-approximation adjusts a Fourier summation to greatly reduce the Gibbs phenomenon, which would otherwise occur at discontinuities. A σ-approximated summation for a series of period T

Finite Legendre transform

The finite Legendre transform (fLT) transforms a mathematical function defined on the finite interval into its Legendre spectrum.Conversely, the inverse fLT (ifLT) reconstructs the original function f

Rounding Errors in Algebraic Processes

No description available.

False precision

False precision (also called overprecision, fake precision, misplaced precision and spurious precision) occurs when numerical data are presented in a manner that implies better precision than is justi

Computational statistics

Computational statistics, or statistical computing, is the bond between statistics and computer science. It means statistical methods that are enabled by using computational methods. It is the area of

Flat pseudospectral method

The flat pseudospectral method is part of the family of the Ross–Fahroo pseudospectral methods introduced by Ross and Fahroo. The method combines the concept of differential flatness with pseudospectr

Compensated CORDIC

No description available.

Numerical smoothing and differentiation

No description available.

Predictor–corrector method

In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differenti

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 accumulated round-o

Round-off error

A roundoff error, also called rounding error, is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-preci

Validated numerics

Validated numerics, or rigorous computation, verified computation, reliable computation, numerical verification (German: Zuverlässiges Rechnen) is numerics including mathematically strict error (round

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathemat

Spectral method

Spectral methods are a class of techniques used in applied mathematics and scientific computing to numerically solve certain differential equations. The idea is to write the solution of the differenti

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 a fun

All-serial CORDIC

No description available.

Isotonic regression

In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing

Rate of convergence

In numerical analysis, the order of convergence and the rate of convergence of a convergent sequence are quantities that represent how quickly the sequence approaches its limit. A sequence that conver

Probability box

A probability box (or p-box) is a characterization of uncertain numbers consisting of both aleatoric and epistemic uncertainties that is often used in risk analysis or quantitative uncertainty modelin

Coopmans approximation

The Coopmans approximation is a method for approximating a fractional-order integrator in a continuous process with constant space complexity. The most correct and accurate methods for calculating the

Explicit algebraic stress model

The algebraic stress model arises in computational fluid dynamics. Two main approaches can be undertaken. In the first, the transport of the turbulent stresses is assumed proportional to the turbulent

Linear multistep method

Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in ti

Interval contractor

In mathematics, an interval contractor (or contractor for short) associated to a set X is an operator C which associates to a box [x] in Rn another box C([x]) of Rn such that the two following propert

Residual (numerical analysis)

Loosely speaking, a residual is the error in a result. To be precise, suppose we want to find x such that Given an approximation x0 of x, the residual is that is, "what is left of the right hand side"

Abramowitz and Stegun

Abramowitz and Stegun (AS) is the informal name of a 1964 mathematical reference work edited by Milton Abramowitz and Irene Stegun of the United States National Bureau of Standards (NBS), now the Nati

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the

Runge–Kutta methods

In numerical analysis, the Runge–Kutta methods (English: /ˈrʊŋəˈkʊtɑː/ RUUNG-ə-KUUT-tah) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discr

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. Trajectories are useful for tracking atmospheric contaminants, s

DCORDIC

No description available.

Unified CORDIC

No description available.

Linear algebra

Linear algebra is the branch of mathematics concerning linear equations such as: linear maps such as: and their representations in vector spaces and through matrices. Linear algebra is central to almo

Forward problem of electrocardiology

The forward problem of electrocardiology is a computational and mathematical approach to study the electrical activity of the heart through the body surface. The principal aim of this study is to comp

Series acceleration

In mathematics, series acceleration is one of a collection of sequence transformations for improving the rate of convergence of a series. Techniques for series acceleration are often applied in numeri

Discretization error

In numerical analysis, computational physics, and simulation, discretization error is the error resulting from the fact that a function of a continuous variable is represented in the computer by a fin

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. The algorithm runs in Θ(n2) time, whi

Singular boundary method

In numerical analysis, the singular boundary method (SBM) belongs to a family of meshless boundary collocation techniques which include the method of fundamental solutions (MFS), boundary knot method

Sparse grid

Sparse grids are numerical techniques to represent, integrate or interpolate high dimensional functions. They were originally developed by the Russian mathematician , a student of Lazar Lyusternik, an

Material point method

The material point method (MPM) is a numerical technique used to simulate the behavior of solids, liquids, gases, and any other continuum material. Especially, it is a robust spatial discretization me

List of numerical analysis topics

This is a list of numerical analysis topics.

Stechkin's lemma

In mathematics – more specifically, in functional analysis and numerical analysis – Stechkin's lemma is a result about the ℓq norm of the tail of a sequence, when the whole sequence is known to have f

Finite difference

A finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by fini

Numerical method

In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming l

Minimax approximation algorithm

A minimax approximation algorithm (or L∞ approximation or uniform approximation) is a method to find an approximation of a mathematical function that minimizes maximum error. For example, given a func

Level set (data structures)

In computer science a level set data structure is designed to represent discretely sampled dynamic level sets functions. A common use of this form of data structure is in efficient image rendering. Th

Whitney inequality

In mathematics, the Whitney inequality gives an upper bound for the error of best approximation of a function by polynomials in terms of the moduli of smoothness. It was first proved by Hassler Whitne

Clenshaw algorithm

In numerical analysis, the Clenshaw algorithm, also called Clenshaw summation, is a recursive method to evaluate a linear combination of Chebyshev polynomials. The method was published by Charles Will

Computer-assisted proof

A computer-assisted proof is a mathematical proof that has been at least partially generated by computer. Most computer-aided proofs to date have been implementations of large proofs-by-exhaustion of

Error analysis (mathematics)

In mathematics, error analysis is the study of kind and quantity of error, or uncertainty, that may be present in the solution to a problem. This issue is particularly prominent in applied areas such

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. The general rules for

Kempner series

The Kempner series is a modification of the harmonic series, formed by omitting all terms whose denominator expressed in base 10 contains the digit 9. That is, it is the sum where the prime indicates

Dynamic relaxation

Dynamic relaxation is a numerical method, which, among other things, can be used to do "" for cable and fabric structures. The aim is to find a geometry where all forces are in equilibrium. In the pas

Ross–Fahroo pseudospectral method

Introduced by I. Michael Ross and F. Fahroo, the Ross–Fahroo pseudospectral methods are a broad collection of pseudospectral methods for optimal control. Examples of the Ross–Fahroo pseudospectral met

Truncation error

In numerical analysis and scientific computing, truncation error is an error caused by approximating a mathematical process.

Quantification of margins and uncertainties

Quantification of Margins and Uncertainty (QMU) is a decision support methodology for complex technical decisions. QMU focuses on the identification, characterization, and analysis of performance thre

Least-squares spectral analysis

Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the mos

Numerical continuation

Numerical continuation is a method of computing approximate solutions of a system of parameterized nonlinear equations, The parameter is usually a real scalar, and the solution an n-vector. For a fixe

Radial basis function interpolation

Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured data, possibly in high-dimensional spaces. The

Overlap–save method

In signal processing, overlap–save is the traditional name for an efficient way to evaluate the discrete convolution between a very long signal and a finite impulse response (FIR) filter : where h[m]

Interval propagation

In numerical mathematics, interval propagation or interval constraint propagation is the problem of contracting interval domains associated to variables of R without removing any value that is consist

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 variables and a fin

Trigonometric tables

In mathematics, tables of trigonometric functions are useful in a number of areas. Before the existence of pocket calculators, trigonometric tables were essential for navigation, science and engineeri

Superconvergence

In numerical analysis, a superconvergent or supraconvergent method is one which converges faster than generally expected (superconvergence or supraconvergence). For example, in the Finite Element Meth

Karlsruhe Accurate Arithmetic

Karlsruhe Accurate Arithmetic (KAA) or Karlsruhe Accurate Arithmetic Approach (KAAA), augments conventional floating-point arithmetic with good error behaviour with new operations to calculate scalar

Timeline of numerical analysis after 1945

The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller histo

Kantorovich theorem

The Kantorovich theorem, or Newton–Kantorovich theorem, is a mathematical statement on the semi-local convergence of Newton's method. It was first stated by Leonid Kantorovich in 1948. It is similar t

Discrete calculus

Discrete calculus or the calculus of discrete functions, is the mathematical study of incremental change, in the same way that geometry is the study of shape and algebra is the study of generalization

Natural element method

The natural element method (NEM) is a meshless method to solve partial differential equation, where the elements do not have a predefined shape as in the finite element method, but depend on the geome

Bueno-Orovio–Cherry–Fenton model

The Bueno-Orovio–Cherry–Fenton model, also simply called Bueno-Orovio model, is a minimal ionic model for human ventricular cells. It belongs to the category of phenomenological models, because of its

Matrix analysis

In mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their algebraic properties. Some particular topics out of many include; operations defined

Boundary knot method

In numerical mathematics, the boundary knot method (BKM) is proposed as an alternative boundary-type meshfree distance function collocation scheme. Recent decades have witnessed a research boom on the

Catastrophic cancellation

In numerical analysis, catastrophic cancellation is the phenomenon that subtracting good approximations to two nearby numbers may yield a very bad approximation to the difference of the original numbe

Multi-time-step integration

In numerical analysis, multi-time-step integration, also referred to as multiple-step or asynchronous time integration, is a numerical time-integration method that uses different time-steps or time-in

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. Note that wh

Calderón projector

In applied mathematics, the Calderón projector is a pseudo-differential operator used widely in boundary element methods. It is named after Alberto Calderón.

Multilevel fast multipole method

The multilevel fast multipole method (MLFMM) is used along with method of moments (MoM) a numerical computational method of solving linear partial differential equations which have been formulated as

Differential-algebraic system of equations

In mathematics, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. Suc

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. It is a fast and efficient method for generating values

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.

Miller's recurrence algorithm

Miller's recurrence algorithm is a procedure for calculating a rapidly decreasing solution of a linear recurrence relation developed by J. C. P. Miller. It was originally developed to compute tables o

Parareal

Parareal is a parallel algorithm from numerical analysis and used for the solution of initial value problems.It was introduced in 2001 by Lions, Maday and Turinici. Since then, it has become one of th

Continuous wavelet

In numerical analysis, continuous wavelets are functions used by the continuous wavelet transform. These functions are defined as analytical expressions, as functions either of time or of frequency.Mo

Interval arithmetic

Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to put bounds on rounding errors and measurement errors in mathema

Linear approximation

In mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences

Sterbenz lemma

In floating-point arithmetic, the Sterbenz lemma or Sterbenz's lemma is a theorem giving conditions under which floating-point differences are computed exactly.It is named after Pat H. Sterbenz, who p

Branching CORDIC

No description available.

Dormand–Prince method

In numerical analysis, the Dormand–Prince (RKDP) method or DOPRI method, is an embedded method for solving ordinary differential equations. The method is a member of the Runge–Kutta family of ODE solv

Galerkin method

In mathematics, in the area of numerical analysis, Galerkin methods, named after the Russian mathematician Boris Galerkin, convert a continuous operator problem, such as a differential equation, commo

Adjoint state method

The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. It has applications in geophysics, seismic imaging,

Bidomain model

The bidomain model is a mathematical model to define the electrical activity of the heart. It consists in a continuum (volume-average) approach in which the cardiac mictrostructure is defined in terms

Pseudospectral knotting method

In applied mathematics, the pseudospectral knotting method is a generalization and enhancement of a standard pseudospectral method for optimal control. The concept was introduced by I. Michael Ross an

Ross' π lemma

Ross' π lemma, named after I. Michael Ross, is a result in computational optimal control. Based on generating Carathéodory-π solutions for feedback control, Ross' π-lemma states that there is fundamen

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-precision floa

Kulisch arithmetic

No description available.

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. The blossom of a polynomial ƒ, often denoted is co

List of operator splitting topics

This is a list of operator splitting topics.

Finite volume method

The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations.In the finite volume method, volume integrals in a partial

Integrable algorithm

Integrable algorithms are numerical algorithms that rely on basic ideas from the mathematical theory of integrable systems.

Pseudo-spectral method

Pseudo-spectral methods, also known as discrete variable representation (DVR) methods, are a class of numerical methods used in applied mathematics and scientific computing for the solution of partial

Shanks transformation

In numerical analysis, the Shanks transformation is a non-linear series acceleration method to increase the rate of convergence of a sequence. This method is named after Daniel Shanks, who rediscovere

Movable cellular automaton

The movable cellular automaton (MCA) method is a method in computational solid mechanics based on the discrete concept. It provides advantages both of classical cellular automaton and discrete element

Gradient discretisation method

In numerical mathematics, the gradient discretisation method (GDM) is a framework which contains classical and recent numerical schemes for diffusion problems of various kinds: linear or non-linear, s

Particle method

In the field of numerical analysis, particle methods discretize fluid into particles. Particle methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computi

Surrogate model

A surrogate model is an engineering method used when an outcome of interest cannot be easily measured or computed, so a model of the outcome is used instead. Most engineering design problems require e

Proper generalized decomposition

The proper generalized decomposition (PGD) is an iterative numerical method for solving boundary value problems (BVPs), that is, partial differential equations constrained by a set of boundary conditi

Riemann solver

A Riemann solver is a numerical method used to solve a Riemann problem. They are heavily used in computational fluid dynamics and computational magnetohydrodynamics.

Kummer's transformation of series

In mathematics, specifically in the field of numerical analysis, Kummer's transformation of series is a method used to accelerate the convergence of an infinite series. The method was first suggested

Pseudo-multiplication

No description available.

2Sum

2Sum is a floating-point algorithm for computing the exact round-off error in a floating-point addition operation. 2Sum and its variant Fast2Sum were first published by Møller in 1965.Fast2Sum is ofte

Boundary particle method

In applied mathematics, the boundary particle method (BPM) is a boundary-only meshless (meshfree) collocation technique, in the sense that none of inner nodes are required in the numerical solution of

Fast multipole method

The fast multipole method (FMM) is a numerical technique that was developed to speed up the calculation of long-ranged forces in the n-body problem. It does this by expanding the system Green's functi

Lie group integrator

A Lie group integrator is a numerical integration method for differential equations built from such as Lie group actions on a manifold. They have been used for the animation and control of vehicles in

Scale co-occurrence matrix

Scale co-occurrence matrix (SCM) is a method for image feature extraction within scale space after wavelet transformation, proposed by Wu Jun and Zhao Zhongming (Institute of Remote Sensing Applicatio

Bernstein's constant

Bernstein's constant, usually denoted by the Greek letter β (beta), is a mathematical constant named after Sergei Natanovich Bernstein and is equal to 0.2801694990... .

Relative change and difference

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a

Chebyshev nodes

In numerical analysis, Chebyshev nodes are specific real algebraic numbers, namely the roots of the Chebyshev polynomials of the first kind. They are often used as nodes in polynomial interpolation be

Hybrid CORDIC

No description available.

Modulus of smoothness

In mathematics, moduli of smoothness are used to quantitatively measure smoothness of functions. Moduli of smoothness generalise modulus of continuity and are used in approximation theory and numerica

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. The name is derived from Oscar Wilde's 1892 play Lady Windermere's Fa

Lanczos approximation

In mathematics, the Lanczos approximation is a method for computing the gamma function numerically, published by Cornelius Lanczos in 1964. It is a practical alternative to the more popular Stirling's

Model order reduction

Model order reduction (MOR) is a technique for reducing the computational complexity of mathematical models in numerical simulations. As such it is closely related to the concept of metamodeling, with

Pythagorean addition

In mathematics, Pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. According to the Pythagorean theorem

Local convergence

In numerical analysis, an iterative method is called locally convergent if the successive approximations produced by the method are guaranteed to converge to a solution when the initial approximation

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. Roughly speaking, the discrepancy of a sequence

Chebyshev pseudospectral method

The Chebyshev pseudospectral method for optimal control problems is based on Chebyshev polynomials of the first kind. It is part of the larger theory of pseudospectral optimal control, a term coined b

Variational multiscale method

The variational multiscale method (VMS) is a technique used for deriving models and numerical methods for multiscale phenomena. The VMS framework has been mainly applied to design stabilized finite el

Regularized meshless method

In numerical mathematics, the regularized meshless method (RMM), also known as the singular meshless method or desingularized meshless method, is a meshless boundary collocation method designed to sol

Jenkins–Traub algorithm

The Jenkins–Traub algorithm for polynomial zeros is a fast globally convergent iterative polynomial root-finding method published in 1970 by and Joseph F. Traub. They gave two variants, one for genera

Significant figures

Significant figures (also known as the significant digits, precision or resolution) of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity

Propagation of uncertainty

In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on the

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. These rules can be use

Basis function

In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as e

The Algebraic Eigenvalue Problem

No description available.

Volder's algorithm

No description available.

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 can involve either inte

Digital Library of Mathematical Functions

The Digital Library of Mathematical Functions (DLMF) is an online project at the National Institute of Standards and Technology (NIST) to develop a database of mathematical reference data for special

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.

Truncated power function

In mathematics, the truncated power function with exponent is defined as In particular, and interpret the exponent as conventional power.

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