# List of numerical analysis topics

This is a list of numerical analysis topics.

## 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

## 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

### Nonlinear programming

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

## 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

## Software

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