Lattice Methods For Multiple Integration
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Lattice Methods For Multiple Integration
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Author : I. H. Sloan
language : en
Publisher: Oxford University Press
Release Date : 1994
Lattice Methods For Multiple Integration written by I. H. Sloan and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
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.
Lattice Rules
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Author : Josef Dick
language : en
Publisher: Springer Nature
Release Date : 2022-08-24
Lattice Rules written by Josef Dick and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-24 with Mathematics categories.
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.
Construction Of Lattice Rules For Multiple Integration Based On A Weighted Discrepancy
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Author : Vasile Sinescu
language : en
Publisher:
Release Date : 2008
Construction Of Lattice Rules For Multiple Integration Based On A Weighted Discrepancy written by Vasile Sinescu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Lattice theory categories.
Randomization Of Lattice Rules For Numerical Multiple Integration
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Author :
language : en
Publisher:
Release Date : 1990
Randomization Of Lattice Rules For Numerical Multiple Integration written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with categories.
The Generation Of Lattice Points For Numerical Multiple Integration
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Author : Stephen Joe
language : en
Publisher:
Release Date : 1987
The Generation Of Lattice Points For Numerical Multiple Integration written by Stephen Joe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Lattice theory categories.
Lattice Rules For Multiple Integration And Discrepance
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Author : Harald Niederreiter
language : en
Publisher:
Release Date : 1989
Lattice Rules For Multiple Integration And Discrepance written by Harald Niederreiter and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Lattice theory categories.
Lattice Methods For Numerical Integration
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Author : M. Beckers
language : en
Publisher:
Release Date : 1991
Lattice Methods For Numerical Integration written by M. Beckers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
The Handbook Of Integration
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Author : Daniel Zwillinger
language : en
Publisher: CRC Press
Release Date : 1992-11-02
The Handbook Of Integration written by Daniel Zwillinger and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-11-02 with Mathematics categories.
This book is a compilation of the most important and widely applicable methods for evaluating and approximating integrals. It is an indispensable time saver for engineers and scientists needing to evaluate integrals in their work. From the table of contents: - Applications of Integration - Concepts and Definitions - Exact Analytical Methods - Approximate Analytical Methods - Numerical Methods: Concepts - Numerical Methods: Techniques
Numerical Integration
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Author : T.O. Espelid
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Numerical Integration written by T.O. Espelid and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
This volume contains refereed papers and extended abstracts of papers presented at the NATO Advanced Research Workshop entitled 'Numerical Integration: Recent Develop ments, Software and Applications', held at the University of Bergen, Bergen, Norway, June 17-21,1991. The Workshop was attended by thirty-eight scientists. A total of eight NATO countries were represented. Eleven invited lectures and twenty-three contributed lectures were presented, of which twenty-five appear in full in this volume, together with three extended abstracts and one note. The main focus of the workshop was to survey recent progress in the theory of methods for the calculation of integrals and show how the theoretical results have been used in software development and in practical applications. The papers in this volume fall into four broad categories: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software. It is five years since the last workshop of this nature was held, at Dalhousie University in Halifax, Canada, in 1986. Recent theoretical developments have mostly occurred in the area of integration rule construction. For polynomial integrating rules, invariant theory and ideal theory have been used to provide lower bounds on the numbers of points for different types of multidimensional rules, and to help in structuring the nonlinear systems which must be solved to determine the points and weights for the rules. Many new optimal or near optimal rules have been found for a variety of integration regions using these techniques.
Random Number Generation And Quasi Monte Carlo Methods
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Author : Harald Niederreiter
language : en
Publisher: SIAM
Release Date : 1992-01-01
Random Number Generation And Quasi Monte Carlo Methods written by Harald Niederreiter and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
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.