Applications of Number Theory to Numerical Analysis

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

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About this book

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.

Table of contents (10 chapters)

  • Algebraic Number Fields and Rational Approximation

    Keng, Hua Loo (et al.)

    Pages 1-27

  • Recurrence Relations and Rational Approximation

    Keng, Hua Loo (et al.)

    Pages 28-47

  • Uniform Distribution

    Keng, Hua Loo (et al.)

    Pages 48-69

  • Estimation of Discrepancy

    Keng, Hua Loo (et al.)

    Pages 70-98

  • Uniform Distribution and Numerical Integration

    Keng, Hua Loo (et al.)

    Pages 99-112

Buy this book

eBook $74.99
price for USA (gross)
  • ISBN 978-3-642-67829-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $99.00
price for USA
  • ISBN 978-3-642-67831-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Applications of Number Theory to Numerical Analysis
Authors
Copyright
1981
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg and Science Press. Beijing
eBook ISBN
978-3-642-67829-5
DOI
10.1007/978-3-642-67829-5
Softcover ISBN
978-3-642-67831-8
Edition Number
1
Number of Pages
X, 244
Topics