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List of numerical analysis topics

From Wikipedia, the free encyclopedia

This is a list of numerical analysis topics.

General

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Error

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Error analysis (mathematics)

Elementary and special functions

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Numerical linear algebra

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

Basic concepts

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Solving systems of linear equations

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Eigenvalue algorithms

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

Other concepts and algorithms

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Interpolation and approximation

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Interpolation — construct a function going through some given data points

Polynomial interpolation

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Polynomial interpolation — interpolation by polynomials

Spline interpolation

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Spline interpolation — interpolation by piecewise polynomials

Trigonometric interpolation

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Trigonometric interpolation — interpolation by trigonometric polynomials

Other interpolants

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Approximation theory

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Approximation theory

Miscellaneous

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Finding roots of nonlinear equations

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See #Numerical linear algebra for linear equations

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

Optimization

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

Basic concepts

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Linear programming

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

Convex optimization

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Convex optimization

Nonlinear programming

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

Optimal control and infinite-dimensional optimization

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Optimal control

Infinite-dimensional optimization

Uncertainty and randomness

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Theoretical aspects

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Applications

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Miscellaneous

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Numerical quadrature (integration)

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Numerical integration — the numerical evaluation of an integral

Numerical methods for ordinary differential equations

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

Numerical methods for partial differential equations

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

Finite difference methods

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

Finite element methods, gradient discretisation methods

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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

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Techniques for improving these methods

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Grids and meshes

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Analysis

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Applications

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Software

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

Journals

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Researchers

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References

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  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.