List of numerical analysis topics


List of numerical analysis topics

This is a list of numerical analysis topics, by Wikipedia page.

Contents

General

Error

Error analysis

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

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

Optimization (mathematics) — 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

Nonlinear programming

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

Uncertainty and randomness

Theoretical aspects

Applications

Miscellaneous

Numerical quadrature (integration)

Numerical integration — the numerical evaluation of an integral

Numerical ordinary differential equations

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

Numerical 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

Finite element method — based on a discretization of the space of solutions

Other methods

Techniques for improving these methods

Miscellaneous

Monte Carlo method

Applications

Software

For software, see the list of numerical analysis software.


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