Numerical analysis

Numerical analysis is the study of algorithms for the problems of continuous mathematics (as distinguished from discrete mathematics). This means it deals mainly with real variable or complex variable questions, numerical linear algebra over the real or complex fields, the solution of differential equations, and other related problems arising in the physical sciences and engineering.

Software

Nowadays, most algorithms are implemented and run on a computer. The Netlib repository contains various collections of software routines for numerical problems, mostly in Fortran and C. Commercial products implementing many different numerical algorithms include the IMSL and NAG libraries; a free alternative is the GNU Scientific Library. A different approach is taken by the Numerical Recipes library, where emphasis is placed on clear understanding of algorithms.

Related Topics:
Netlib - Fortran - C - IMSL - GNU Scientific Library - Numerical Recipes

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Other popular languages for numerical computations are MATLAB, IDL, and Python. These are interpreted programming languages, but they allow for faster development and prototyping, and if necessary can be converted to Fortran and C for enhanced speed.

Related Topics:
MATLAB - IDL - Python - Interpreted programming language

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Many computer algebra systems such as Mathematica or Maple (free software systems include Maxima, Axiom, calc and Yacas), can also be used for numerical computations. However, their strength typically lies in symbolic computations.

Related Topics:
Computer algebra system - Mathematica - Maple - Free software - Maxima - Axiom - Calc - Yacas

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