Table of contents

  1. Front Matter
    Pages i-ix
  2. Hua Loo Keng, Wang Yuan
    Pages 1-27
  3. Hua Loo Keng, Wang Yuan
    Pages 28-47
  4. Hua Loo Keng, Wang Yuan
    Pages 48-69
  5. Hua Loo Keng, Wang Yuan
    Pages 70-98
  6. Hua Loo Keng, Wang Yuan
    Pages 99-112
  7. Hua Loo Keng, Wang Yuan
    Pages 113-130
  8. Hua Loo Keng, Wang Yuan
    Pages 131-158
  9. Hua Loo Keng, Wang Yuan
    Pages 159-182
  10. Hua Loo Keng, Wang Yuan
    Pages 183-203
  11. Back Matter
    Pages 224-244

About this book

Introduction

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.

Keywords

Applications Numerische Mathematik Zahlentheorie calculus computer number theory numerical analysis

Authors and affiliations

  • Hua Loo Keng
    • 1
  • Wang Yuan
    • 1
  1. 1.Institute of MathematicsAcademia SinicaBeijingThe People’s Republic of China

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-67829-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1981
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-67831-8
  • Online ISBN 978-3-642-67829-5
  • About this book