List of numerical analysis topics

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This is a list of numerical analysis topics.



Error analysis (mathematics)

Elementary and special functions[edit]

Numerical linear algebra[edit]

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

Basic concepts[edit]

Solving systems of linear equations[edit]

Eigenvalue algorithms[edit]

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

Other concepts and algorithms[edit]

Interpolation and approximation[edit]

Interpolation — construct a function going through some given data points

Polynomial interpolation[edit]

Polynomial interpolation — interpolation by polynomials

Spline interpolation[edit]

Spline interpolation — interpolation by piecewise polynomials

Trigonometric interpolation[edit]

Trigonometric interpolation — interpolation by trigonometric polynomials

Other interpolants[edit]

Approximation theory[edit]

Approximation theory


Finding roots of nonlinear equations[edit]

See #Numerical linear algebra for linear equations

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


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

Basic concepts[edit]

Linear programming[edit]

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

Convex optimization[edit]

Convex optimization

Nonlinear programming[edit]

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

Optimal control and infinite-dimensional optimization[edit]

Optimal control

Infinite-dimensional optimization

Uncertainty and randomness[edit]

Theoretical aspects[edit]



Numerical quadrature (integration)[edit]

Numerical integration — the numerical evaluation of an integral

Numerical methods for ordinary differential equations[edit]

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

Numerical methods for partial differential equations[edit]

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

Finite difference methods[edit]

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

Finite element methods, gradient discretisation methods[edit]

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[edit]

Techniques for improving these methods[edit]

Grids and meshes[edit]


Monte Carlo method[edit]



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




  1. ^ Smith, N. J. J. (2008). "Worldly Vagueness and Semantic Indeterminacy". Vagueness and Degrees of Truth. pp. 277–316. doi:10.1093/acprof:oso/9780199233007.003.0007. ISBN 9780199233007.