Applications of Number Theory to Numerical Analysis

S. K. Zaremba

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780127759500
• eBook ISBN:
  9781483265162
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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

• Front Cover
• Applications of Number Theory to Numerical Analysis
• Copyright Page
• Table of Contents
• CONTRIBUTORS
• PREFACE
• Chapter 1. Some Combinatorial Problems Studied Experimentally on Computing Machines
• Chapter 2. Experiments on Optimal Coefficients
• Chapter 3. 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
• Chapter 4. Recherche et Utilisation des "Bons Treillis." Programmation et Résultats Numériques
• English Summary: Search for, and Applications of, "Good Lattices," Programming and Numerical Results
• Chapter 5. Methods for Estimating Discrepancy
• Chapter 6. A Distribution Problem in Finite Sets
• Chapter 7. The Structure of Linear Congruential Sequences
• Chapter 8. Statistical Interdependence of Pseudo-Random Numbers Generated by the Linear Congruential Method
• Chapter 9. Computational Investigations of Low-Discrepancy Point Sets
• Chapter 10. Estimating the Accuracy of Quasi-Monte Carlo Integration
• Chapter 11. Lattice Structure and Reduced Bases of Random Vectors Generated by Linear Recurrences
• Chapter 12. A Transformation of Equidistributed Sequences
• Chapter 13. On the Second Round of the Maximal Order Program
• Chapter 14. Modulo Optimization Problems and Integer Linear Programming
• Chapter 15. Equivalent Forms of Zero-One Programs
• Chapter 16. Incidence Matrices of Boolean Functions and Zero-One Programming
• Chapter 17. Number Theoretic Foundations of Finite Precision Arithmetic