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 $\text { 1 }$ ... (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
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): numerical analysis