Applications of Number Theory to Numerical Analysis L. -K Hua

ISBN: 9783642678318

Published: November 15th 2011

Paperback

244 pages


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Applications of Number Theory to Numerical Analysis  by  L. -K Hua

Applications of Number Theory to Numerical Analysis by L. -K Hua
November 15th 2011 | Paperback | PDF, EPUB, FB2, DjVu, audiobook, mp3, ZIP | 244 pages | ISBN: 9783642678318 | 7.40 Mb

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 importantMoreOwing 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. Itor 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 1950s. 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.



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