List of numerical analysis topics

This is a list of numerical analysis topics.

Error analysis

Numerical linear algebra

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

Eigenvalue algorithms

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

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

Approximation theory

Approximation theory

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

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

Miscellaneous

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

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

Software

For software, see the list of numerical analysis software.