Standard Article

Numerical Analysis

  1. Gordon K. Smyth

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a14025

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Smyth, G. K. 2005. Numerical Analysis. Encyclopedia of Biostatistics. 6.

Author Information

  1. Walter and Eliza Hall Institute of Medical Research, Melbourne, Victoria, Australia

Publication History

  1. Published Online: 15 JUL 2005

Abstract

Numerical analysis is concerned with the accurate and efficient evaluation of mathematical expressions, especially on computers with floating point arithmetic. This article discusses the fundamental ideas of numerical accuracy including rounding error, approximation error, conditioning, and stability. The problem of computing a sample variance is considered as a simple illustrative example. The article goes on to describe briefly a number of key topics in numerical analysis, which are treated in more depth in separate articles, including linear equations and matrix computations, optimization and nonlinear equations, interpolation and approximation, and numerical integration. Brief pointers are given to available software.

Keywords:

  • condition number;
  • ill-conditioning;
  • numerical stability;
  • floating point arithmetic;
  • floating point operations;
  • rounding error;
  • subtractive cancellation;
  • approximation error