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Author :
Publisher :
ISBN 13 :
Total Pages : 9 pages
Book Rating : 4.:/5 (22 download)
Download or read book Randomization of lattice rules for numerical multiple integration written by and published by . This book was released on 1990 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : I. H. Sloan
Publisher : Oxford University Press
ISBN 13 : 9780198534723
Total Pages : 256 pages
Book Rating : 4.5/5 (347 download)
Download or read book Lattice Methods for Multiple Integration written by I. H. Sloan and published by Oxford University Press. This book was released on 1994 with total page 256 pages. 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
Publisher : Springer Nature
ISBN 13 : 3031099516
Total Pages : 584 pages
Book Rating : 4.0/5 (31 download)
Download or read book Lattice Rules written by Josef Dick and published by Springer Nature. This book was released on 2022-08-24 with total page 584 pages. 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 : Harald Niederreiter
Publisher : SIAM
ISBN 13 : 9781611970081
Total Pages : 247 pages
Book Rating : 4.9/5 (7 download)
Download or read book Random Number Generation and Quasi-Monte Carlo Methods written by Harald Niederreiter and published by SIAM. This book was released on 1992-01-01 with total page 247 pages. 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.
Author : Nancy Flournoy
Publisher : American Mathematical Soc.
ISBN 13 : 0821851225
Total Pages : 290 pages
Book Rating : 4.8/5 (218 download)
Download or read book Statistical Multiple Integration written by Nancy Flournoy and published by American Mathematical Soc.. This book was released on 1991 with total page 290 pages. 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
Publisher :
ISBN 13 :
Total Pages : 19 pages
Book Rating : 4.:/5 (22 download)
Download or read book Lattice Rules for Multiple Integration and Discrepance written by Harald Niederreiter and published by . This book was released on 1989 with total page 19 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Vasile Sinescu
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.:/5 (243 download)
Download or read book Construction of Lattice Rules for Multiple Integration Based on a Weighted Discrepancy written by Vasile Sinescu and published by . This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Igor Shparlinski
Publisher : Springer Science & Business Media
ISBN 13 : 940111806X
Total Pages : 253 pages
Book Rating : 4.4/5 (11 download)
Download or read book Computational and Algorithmic Problems in Finite Fields written by Igor Shparlinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
Author : Alan Genz
Publisher : Springer Science & Business Media
ISBN 13 : 3642016898
Total Pages : 130 pages
Book Rating : 4.6/5 (42 download)
Download or read book Computation of Multivariate Normal and t Probabilities written by Alan Genz and published by Springer Science & Business Media. This book was released on 2009-07-09 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multivariate normal and t probabilities are needed for statistical inference in many applications. Modern statistical computation packages provide functions for the computation of these probabilities for problems with one or two variables. This book describes recently developed methods for accurate and efficient computation of the required probability values for problems with two or more variables. The book discusses methods for specialized problems as well as methods for general problems. The book includes examples that illustrate the probability computations for a variety of applications.
Author : Samuel Kotz
Publisher : Cambridge University Press
ISBN 13 : 9780521826549
Total Pages : 296 pages
Book Rating : 4.8/5 (265 download)
Download or read book Multivariate T-Distributions and Their Applications written by Samuel Kotz and published by Cambridge University Press. This book was released on 2004-02-16 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Almost all the results available in the literature on multivariate t-distributions published in the last 50 years are now collected together in this comprehensive reference. Because these distributions are becoming more prominent in many applications, this book is a must for any serious researcher or consultant working in multivariate analysis and statistical distributions. Much of this material has never before appeared in book form. The first part of the book emphasizes theoretical results of a probabilistic nature. In the second part of the book, these are supplemented by a variety of statistical aspects. Various generalizations and applications are dealt with in the final chapters. The material on estimation and regression models is of special value for practitioners in statistics and economics. A comprehensive bibliography of over 350 references is included.
Author : Harald Niederreiter
Publisher : Springer Science & Business Media
ISBN 13 : 1461225523
Total Pages : 391 pages
Book Rating : 4.4/5 (612 download)
Download or read book Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing written by Harald Niederreiter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientists and engineers are increasingly making use of simulation methods to solve problems which are insoluble by analytical techniques. Monte Carlo methods which make use of probabilistic simulations are frequently used in areas such as numerical integration, complex scheduling, queueing networks, and large-dimensional simulations. This collection of papers arises from a conference held at the University of Nevada, Las Vegas, in 1994. The conference brought together researchers across a range of disciplines whose interests include the theory and application of these methods. This volume provides a timely survey of this field and the new directions in which the field is moving.
Author :
Publisher :
ISBN 13 :
Total Pages : 828 pages
Book Rating : 4.3/5 (121 download)
Download or read book SIAM Journal on Numerical Analysis written by and published by . This book was released on 2002-12 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Arnold R. Krommer
Publisher : Springer Science & Business Media
ISBN 13 : 9783540584100
Total Pages : 366 pages
Book Rating : 4.5/5 (841 download)
Download or read book Numerical Integration written by Arnold R. Krommer and published by Springer Science & Business Media. This book was released on 1994-09-28 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topics in this volume constitute a fitting tribute by distinguished physicists and mathematicians. They cover strings, conformal field theories, W and Virasoro algebras, topological field theory, quantum groups, vertex and Hopf algebras, and non-commutative geometry. The relatively long contributions are pedagogical in style and address students as well as scientists.
Author : Stephen Joe
Publisher :
ISBN 13 :
Total Pages : 10 pages
Book Rating : 4.:/5 (22 download)
Download or read book The Generation of Lattice Points for Numerical Multiple Integration written by Stephen Joe and published by . This book was released on 1987 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Christiane Lemieux
Publisher : Springer Science & Business Media
ISBN 13 : 038778165X
Total Pages : 373 pages
Book Rating : 4.3/5 (877 download)
Download or read book Monte Carlo and Quasi-Monte Carlo Sampling written by Christiane Lemieux and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi–Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. Their successful implementation on practical problems, especially in finance, has motivated the development of several new research areas within this field to which practitioners and researchers from various disciplines currently contribute. This book presents essential tools for using quasi–Monte Carlo sampling in practice. The first part of the book focuses on issues related to Monte Carlo methods—uniform and non-uniform random number generation, variance reduction techniques—but the material is presented to prepare the readers for the next step, which is to replace the random sampling inherent to Monte Carlo by quasi–random sampling. The second part of the book deals with this next step. Several aspects of quasi-Monte Carlo methods are covered, including constructions, randomizations, the use of ANOVA decompositions, and the concept of effective dimension. The third part of the book is devoted to applications in finance and more advanced statistical tools like Markov chain Monte Carlo and sequential Monte Carlo, with a discussion of their quasi–Monte Carlo counterpart. The prerequisites for reading this book are a basic knowledge of statistics and enough mathematical maturity to follow through the various techniques used throughout the book. This text is aimed at graduate students in statistics, management science, operations research, engineering, and applied mathematics. It should also be useful to practitioners who want to learn more about Monte Carlo and quasi–Monte Carlo methods and researchers interested in an up-to-date guide to these methods.
Author : Giray Okten
Publisher : Universal-Publishers
ISBN 13 : 1581120419
Total Pages : 91 pages
Book Rating : 4.5/5 (811 download)
Download or read book Contributions to the Theory of Monte Carlo and Quasi-Monte Carlo Methods written by Giray Okten and published by Universal-Publishers. This book was released on 1999 with total page 91 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi-Monte Carlo methods, which are often described as deterministic versions of Monte Carlo methods, were introduced in the 1950s by number theoreticians. They improve several deficiencies of Monte Carlo methods; such as providing estimates with deterministic bounds and avoiding the paradoxical difficulty of generating random numbers in a computer. However, they have their own drawbacks. First, although they provide faster convergence than Monte Carlo methods asymptotically, the advantage may not be practical to obtain in "high" dimensional problems. Second, there is not a practical way to measure the error of a quasi-Monte Carlo simulation. Finally, unlike Monte Carlo methods, there is a scarcity of error reduction techniques for these methods. In this dissertation, we attempt to provide remedies for the disadvantages of quasi-Monte Carlo methods mentioned above. In the first part of the dissertation, a hybrid-Monte Carlo sequence designed to obtain error reduction in high dimensions is studied. Probabilistic results on the discrepancy of this sequence as well as results obtained by applying the sequence to problems from numerical integration and mathematical finance are presented. In the second part of the dissertation, a new hybrid-Monte Carlo method is introduced, in an attempt to obtain a practical statistical error analysis using low-discrepancy sequences. It is applied to problems from mathematical finance and particle transport theory to compare its effectiveness with the conventional methods. In the last part of the dissertation, a generalized quasi-Monte Carlo integration rule is introduced. A Koksma-Hlawka type inequality for the rule is proved, using a new concept for the variation of a function. As a consequence of the rule, error reduction techniques and in particular an "importance sampling" type statement are derived. Problems from different disciplines are used as practical tests for our methods. The numerical results obtained in favor of the methods suggest the practical advantages that can be realized by their use in a wide variety of applications.
Author :
Publisher :
ISBN 13 :
Total Pages : 1402 pages
Book Rating : 4.:/5 (318 download)
Download or read book SIAM Journal on Scientific Computing written by and published by . This book was released on 2008 with total page 1402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
