Applications of Number Theory to Numerical Analysis - 1st Edition - ISBN: 9780127759500, 9781483265162

Applications of Number Theory to Numerical Analysis

1st Edition

Editors: S. K. Zaremba
eBook ISBN: 9781483265162
Imprint: Academic Press
Published Date: 1st January 1972
Page Count: 504
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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




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


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© Academic Press 1972
Academic Press
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About the Editor

S. K. Zaremba

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