# Definition:Numerical Analysis

## Definition

Numerical analysis is the branch of applied mathematics concerned with the processes by which certain kinds of numerical solutions to problems in (mainly) physics.

### Motivation

It is impossible to write down an exact decimal representation of a solution to certain equations, as they may be irrational.

Certain other problems are defined by equations which cannot be solved using analytical methods.

Hence:

The aim of numerical methods is to provide practical procedures for calculating the solutions of problems in applied mathematics to a specified degree of accuracy.
-- B. Noble: Numerical Methods: Volume $\text { 1 }$

To produce a number which answers a problem is only one aspect of the topic of numerical analysis.

The other aspect, usually more difficult, is to ensure that the answer is correct within particular stated limits.

## Also known as

Numerical analysis is often referred to as numerical methods.

## Also see

• Results about numerical analysis can be found here.

## Historical Note

As a result of the development since the middle of the $20$th century of the electronic computer, the discipline of numerical analysis has greatly increased in importance.

It is now possible to directly model the behaviour of an artefact by simulation to a high level of accuracy.