Order Stars : Theory and Applications

ISBN-13: 9780412352607 / Angielski / Twarda / 1991 / 248 str.

A. Iserles; Iserles Iserles; S. P. Norsett

Opis

Order stars is a recently developed technique to analyze and explain the behaviour of numerical methods. The main idea is to explore different features of numerical algorithms as properties of analytical functions in various portions of the complex plane. Thus, for example, the order of some numerical methods for ordinary differential equations can be translated to the language of approximation theory - specifically, to the question of how well a given rational function R approximates the exponential. Likewise, stability properties of the underlying method can be expressed as some other features of the function R. In this formulation, order stars establish the relationship between order and stability, helping in the search for better and more efficient computational algorithms.

Spis treści

1. Introduction 2. General order stars 3. Rational approximants to the exponential 4. A-acceptability barriers 5. Multistep methods 6. The advection equation 7. The diffusion equation 8. Pade approximants 9. Contractive approximation 10. Open problems

O autorze

A. Iserles (University of Cambridge) (Author) , S.P. Norsett (Author)