Numerical Analysis

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 a..