Definition:Numerical Analysis/Motivation

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.

-- 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.

Sources

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