Applications of Number Theory to Numerical Analysis

Hua, L.-K. und Y. Wang:

ISBN 10: 3540103821 / ISBN 13: 9783540103820

Published by Springer, 1981

About this Item

254 P Unread book. Very good condition. Minimum traces of storage. 9783540103820 Sprache: Englisch Gewicht in Gramm: 558.

Seller Inventory # 203502

Bibliographic Details

• Title: Applications of Number Theory to Numerical Analysis
• Publisher: Springer
• Publication Date: 1981
• Language: English
• ISBN 10: 3540103821
• ISBN 13: 9783540103820
• Binding: Hardcover
• Edition: 1.
• Seller catalogs:
  • Mathematik

About this title

Synopsis

Owing to the developments and applications of computer science, ma­ thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically as well as satisfactory from the theoretical view point. It'or example, from the seventeenth century till now, a great deal of effort was made in developing methods for approximating single integrals and there were only a few works on multiple quadrature until the 1950's. But in the past twenty years, a number of new methods have been devised of which the number theoretic method is an effective one. The number theoretic method may be described as follows. We use num­ ber theory to construct a sequence of uniformly distributed sets in the s­ dimensional unit cube G , where s ~ 2. Then we use the sequence to s reduce a difficult analytic problem to an arithmetic problem which may be calculated by computer. For example, we may use the arithmetic mean of the values of integrand in a given uniformly distributed set of G to ap­ s proximate the definite integral over G such that the principal order of the s error term is shown to be of the best possible kind, if the integrand satis­ fies certain conditions.