# 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.*

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.

## Sources

- 1958: D.R. Hartree:
*Numerical Analysis*(2nd ed.) ... (next): Chapter $\text {I}$: Introduction: $1.1$. What numerical analysis is about - 1964: B. Noble:
*Numerical Methods: Volume $\text { 1 }$*... (previous) ... (next): Chapter $\text I$: Accuracy and Error: $\S 1.1$. Introduction - 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): Miscellaneous Problems for Chapter $2$: Appendix $\text{A}$. Numerical Methods - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**numerical analysis** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**numerical analysis** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**numerical analysis**