List of numerical analysis topics

This is a list of numerical analysis topics.

General

Error

Error analysis (mathematics)

Elementary and special functions

Numerical linear algebra

Numerical linear algebra — study of numerical algorithms for linear algebra problems

Basic concepts

Solving systems of linear equations

Eigenvalue algorithms

Eigenvalue algorithm — a numerical algorithm for locating the eigenvalues of a matrix

Other concepts and algorithms

Interpolation and approximation

Interpolation — construct a function going through some given data points

Polynomial interpolation

Polynomial interpolation — interpolation by polynomials

Spline interpolation

Spline interpolation — interpolation by piecewise polynomials

Trigonometric interpolation

Trigonometric interpolation — interpolation by trigonometric polynomials

Other interpolants

Approximation theory

Approximation theory

Miscellaneous

Finding roots of nonlinear equations

See #Numerical linear algebra for linear equations

Root-finding algorithm — algorithms for solving the equation f(x) = 0

Optimization

Mathematical optimization — algorithm for finding maxima or minima of a given function

Basic concepts

Linear programming

Linear programming (also treats integer programming) — objective function and constraints are linear

Convex optimization

Convex optimization

Nonlinear programming

Nonlinear programming — the most general optimization problem in the usual framework

Optimal control and infinite-dimensional optimization

Optimal control

Infinite-dimensional optimization

Uncertainty and randomness

Theoretical aspects

Applications

Miscellaneous

Numerical quadrature (integration)

Numerical integration — the numerical evaluation of an integral

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations — the numerical solution of ordinary differential equations (ODEs)

Numerical methods for partial differential equations

Numerical partial differential equations — the numerical solution of partial differential equations (PDEs)

Finite difference methods

Finite difference method — based on approximating differential operators with difference operators

Finite element methods, gradient discretisation methods

Finite element method — based on a discretization of the space of solutions gradient discretisation method — based on both the discretization of the solution and of its gradient

Other methods

Techniques for improving these methods

Grids and meshes

Analysis

Monte Carlo method

Applications

Software

For a large list of software, see the list of numerical analysis software.

Journals

Researchers

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