Numerical analysis

INTRODUCTION

Numerical analysis uses computation as a tool to investigate mathematical models. At its most basic, this might mean computing an answer, such as the optimal value of a linear program. Beyond this, one might want error estimates (how accurate is the optimal value computed by the algorithm) or sensitivity information (how sensitive is the optimal value to changes in the data). One might even wish to analyze the effects of randomness in the data. Numerical analysis can also be used as an experimental tool (perhaps combined with computer graphics) to reveal properties of models that may be inaccessible by analytic means.

The techniques of numerical analysis have been widely adopted. It is rare for someone to solve a linear program by hand — except perhaps in a class-room. Large-scale simulations would be all but impossible without the aid of a computer. For many people, numerical techniques have superseded analytic techniques as a tool for solving mathematical problems. There...