# Definition:Numerical Analysis/Motivation

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## Numerical Analysis: 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.

## Sources

- 1964: B. Noble:
*Numerical Methods: Volume $\text { 1 }$*... (previous) ... (next): Chapter $\text I$: Accuracy and Error: $\S 1.1$. Introduction