Applications of number theory to numerical analysis

Includes index

Includes bibliography (p. 489) and references

Some combinatorial problems studied experimentally on computing machines / S. M. Ulam
Experiments on optimal coefficients / Seymour Haber
Methode des "bons treillis" pour le calcul des integrales multiples / S. K Zaremba
English Summary: The Method of "Good Lattices" for the Numerical Computation of Multiple Integrals
Recherche et utilisation des "bons treillis." programmation et resultats numeriques / Dominique Maisonneuve
English Summary: Search for, and Applications of, "Good Lattices," Programming and Numerical Results
Methods for estimating discrepancy / H. Niederreiter
Distribution problem in finite sets / H. Niederreiter
Structure of linear congruential sequences / George Marsaglia
Statistical interdependence of pseudo-random numbers generated by the linear congruential method / U. Dieter
Computational investigations of low-discrepancy point sets / Tony T. Warnock
Estimating the accuracy of quasi-monte carlo integration / John H. Halton
Lattice structure and reduced bases of random vectors generated by linear recurrences / W. A. Beyer
Transformation of equidistributed sequences / E. Hlawka and R. Milek
On the second round of the maximal order program / Hans Zassenhaus
Modulo optimization problems and integer linear programming / Gordon H Bradley
Equivalent forms of zero-one programs / Peter L. Hammer and lvo G. Rosenberg
Incidence matrices of boolean functions and zero-one programming / Abraham Berman
Number theoretic foundations of finite precision arithmetic / D. W. Matula

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.