Applications of Number Theory to Numerical Analysis

Applications of Number Theory to Numerical Analysis

1st Edition - January 1, 1972

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  • Editor: S. K. Zaremba
  • eBook ISBN: 9781483265162

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Description

Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.

Table of Contents


  • Contributors

    Préface

    Preface

    Some Combinatorial Problems Studied Experimentally on Computing Machines

    Experiments on Optimal Coefficients

    La Méthode des "Bons Treillis" Pour le Calcul des Intégrales Multiples

    English Summary: The Method of "Good Lattices" for the Numerical Computation of Multiple Integrals

    Recherche et Utilisation des "Bons Treillis." Programmation et Résultats Numériques

    English Summary: Search for, and Applications of, "Good Lattices," Programming and Numerical Results

    Methods for Estimating Discrepancy

    A Distribution Problem in Finite Sets

    The Structure of Linear Congruential Sequences

    Statistical Interdependence of Pseudo-Random Numbers Generated by the Linear Congruential Method

    Computational Investigations of Low-Discrepancy Point Sets

    Estimating the Accuracy of Quasi-Monte Carlo Integration

    Lattice Structure and Reduced Bases of Random Vectors Generated by Linear Recurrences

    A Transformation of Equidistributed Sequences

    On the Second Round of the Maximal Order Program

    Modulo Optimization Problems and Integer Linear Programming

    Equivalent Forms of Zero-One Programs

    Incidence Matrices of Boolean Functions and Zero-One Programming

    Number Theoretic Foundations of Finite Precision Arithmetic

Product details

  • No. of pages: 504
  • Language: English
  • Copyright: © Academic Press 1972
  • Published: January 1, 1972
  • Imprint: Academic Press
  • eBook ISBN: 9781483265162

About the Editor

S. K. Zaremba

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