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Author :
Release : 1990
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Randomization of lattice rules for numerical multiple integration by :
Download or read book Randomization of lattice rules for numerical multiple integration written by . This book was released on 1990. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I. H. Sloan
Release : 1994
Genre : Mathematics
Kind : eBook
Book Rating : 723/5 ( reviews)
Book Synopsis Lattice Methods for Multiple Integration by : I. H. Sloan
Download or read book Lattice Methods for Multiple Integration written by I. H. Sloan. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book devoted to lattice methods, a recently developed way of calculating multiple integrals in many variables. Multiple integrals of this kind arise in fields such as quantum physics and chemistry, statistical mechanics, Bayesian statistics and many others. Lattice methods are an effective tool when the number of integrals are large. The book begins with a review of existing methods before presenting lattice theory in a thorough, self-contained manner, with numerous illustrations and examples. Group and number theory are included, but the treatment is such that no prior knowledge is needed. Not only the theory but the practical implementation of lattice methods is covered. An algorithm is presented alongside tables not available elsewhere, which together allow the practical evaluation of multiple integrals in many variables. Most importantly, the algorithm produces an error estimate in a very efficient manner. The book also provides a fast track for readers wanting to move rapidly to using lattice methods in practical calculations. It concludes with extensive numerical tests which compare lattice methods with other methods, such as the Monte Carlo.
Author : Josef Dick
Release : 2022-08-24
Genre : Mathematics
Kind : eBook
Book Rating : 516/5 ( reviews)
Book Synopsis Lattice Rules by : Josef Dick
Download or read book Lattice Rules written by Josef Dick. This book was released on 2022-08-24. Available in PDF, EPUB and Kindle. Book excerpt: Lattice rules are a powerful and popular form of quasi-Monte Carlo rules based on multidimensional integration lattices. This book provides a comprehensive treatment of the subject with detailed explanations of the basic concepts and the current methods used in research. This comprises, for example, error analysis in reproducing kernel Hilbert spaces, fast component-by-component constructions, the curse of dimensionality and tractability, weighted integration and approximation problems, and applications of lattice rules.
Author : Nancy Flournoy
Release : 1991
Genre : Mathematics
Kind : eBook
Book Rating : 225/5 ( reviews)
Book Synopsis Statistical Multiple Integration by : Nancy Flournoy
Download or read book Statistical Multiple Integration written by Nancy Flournoy. This book was released on 1991. Available in PDF, EPUB and Kindle. Book excerpt: High dimensional integration arises naturally in two major sub-fields of statistics: multivariate and Bayesian statistics. Indeed, the most common measures of central tendency, variation, and loss are defined by integrals over the sample space, the parameter space, or both. Recent advances in computational power have stimulated significant new advances in both Bayesian and classical multivariate statistics. In many statistical problems, however, multiple integration can be the major obstacle to solutions. This volume contains the proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Statistical Multiple Integration, held in June 1989 at Humboldt State University in Arcata, California. The conference represents an attempt to bring together mathematicians, statisticians, and computational scientists to focus on the many important problems in statistical multiple integration. The papers document the state of the art in this area with respect to problems in statistics, potential advances blocked by problems with multiple integration, and current work directed at expanding the capability to integrate over high dimensional surfaces.
Author : Harald Niederreiter
Release : 1992-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 081/5 ( reviews)
Book Synopsis Random Number Generation and Quasi-Monte Carlo Methods by : Harald Niederreiter
Download or read book Random Number Generation and Quasi-Monte Carlo Methods written by Harald Niederreiter. This book was released on 1992-01-01. Available in PDF, EPUB and Kindle. Book excerpt: Tremendous progress has taken place in the related areas of uniform pseudorandom number generation and quasi-Monte Carlo methods in the last five years. This volume contains recent important work in these two areas, and stresses the interplay between them. Some developments contained here have never before appeared in book form. Includes the discussion of the integrated treatment of pseudorandom numbers and quasi-Monte Carlo methods; the systematic development of the theory of lattice rules and the theory of nets and (t,s)-sequences; the construction of new and better low-discrepancy point sets and sequences; Nonlinear congruential methods; the initiation of a systematic study of methods for pseudorandom vector generation; and shift-register pseudorandom numbers. Based on a series of 10 lectures presented by the author at a CBMS-NSF Regional Conference at the University of Alaska at Fairbanks in 1990 to a selected group of researchers, this volume includes background material to make the information more accessible to nonspecialists.
