Applications of number theory to numerical analysis: Applications de la théorie des nombres á l'analyse numérique

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. Content: Inside Front Cover, Page ii Front Matter, Page iii Copyright, Page iv CONTRIBUTORS, Pages vii-viii PREFACE, Pages ix-x PREFACE, Pages xi-xii Some Combinatorial Problems Studied Experimentally on Computing Machines, Pages 1-10, S.M. ULAM Experiments on Optimal Coefficients, Pages 11-37, SEYMOUR HABER La Méthode des “Bons Treillis” pour le Calcul des Intégrales Multiples, Pages 39-119, S.K. ZAREMBA Recherche et Utilisation des “Bons Treillis.” Programmation et Résultats Numériques, Pages 121-201, DOMINIQUE MAISONNEUVE Methods for Estimating Discrepancy, Pages 203-236, H. NIEDERREITER A Distribution Problem in Finite Sets, Pages 237-248, H. NIEDERREITER The Structure of Linear Congruential Sequences, Pages 249-285, GEORGE MARSAGLIA Statistical Interdependence of Pseudo-Random Numbers Generated by the Linear Congruential Method, Pages 287-317, U. DIETER Computational Investigations of Low-Discrepancy Point Sets, Pages 319-343, TONY T. WARNOCK Estimating the Accuracy of Quasi-Monte Carlo Integration, Pages 345-360, JOHN H. HALTON Lattice Structure and Reduced Bases of Random Vectors Generated by Linear Recurrences, Pages 361-370, W.A. BEYER A Transformation of Equidistributed Sequences, Pages 371-388, E. HLAWKA, R. MÜCK On the Second Round of the Maximal Order Program, Pages 389-431, HANS ZASSENHAUS Modulo Optimization Problems and Integer Linear Programming, Pages 433-451, GORDON H. BRADLEY Equivalent Forms of Zero-One Programs, Pages 453-463, PETER L. HAMMER, IVO G. ROSENBERG Incidence Matrices of Boolean Functions and Zero-One Programming, Pages 465-477, ABRAHAM BERMAN Number Theoretic Foundations of Finite Precision Arithmetic, Pages 479-489, D.W. MATULA Edited By S. K. Zaremba. Proceedings Of The Symposium At The Centre For Research In Mathematics, University Of Montreal, September 9-14, 1971. English Or French; French Papers With Summaries In English. Includes Bibliographies.