The state of the art in numerical analysis, 1986: A. Iserles and M.J.D. Powell, eds., IMA Conference Series (New Series), Clarendon Press, Oxford, 1987. ISBN 0-19-8536143. £ 55 (hard cover).

✍ Scribed by David F. Griffiths

• Publisher: Elsevier Science
• Year: 1987
• Tongue: English
• Weight: 204 KB
• Volume: 47
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(87)90122-6

✦ Synopsis

Numerical Analysis, if one were to judge by the diverse use that is made of numerical methods, could be mistaken for an incoherent discipline. It is true that its tentacles spread throughout the scientific, engineering, industrial and commercial communities but, at its heart, it is concerned with the study of relatively few core topics: the solution of linear and nonlinear algebraic equations, integral and differential equations, optimization and the approximation of functions and data. Although the numerical aspects of these topics are often studied as a branch of mathematics, the more common view of a numerical analyst is one who devises and analyses methods for solving standard problems within these areas. Since the methods are often used by those with little mathematical or numerical sophistication, great emphasis has to be placed on robustness and reliability. Such is the situation that has to be catered for in numerical linear algebra and certain areas of optimization for example. Where the underlying models are more mathematically sophisticated, typically in differential and integral equations, there is more input from users. Practitioners feel free to devise new methods on the basis of physical intuition and numerical experience. This adds vitality to the subject because, by extracting the essential features of successful algorithms in one area, they can be included in the standard armoury and disseminated to a wider audience.