Lattice Rules For Multiple Integration And Discrepance
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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.
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.
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.
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.
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.
Digital Lattice Rules
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Author : Josef Dick
language : en
Publisher:
Release Date : 2004
Digital Lattice Rules written by Josef Dick and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Function spaces categories.
Sequences Discrepancies And Applications
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Author : Michael Drmota
language : en
Publisher: Springer
Release Date : 2006-11-14
Sequences Discrepancies And Applications written by Michael Drmota and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.
Computational Integration
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Author : Arnold R. Krommer
language : en
Publisher: SIAM
Release Date : 1998-01-01
Computational Integration written by Arnold R. Krommer and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
This survey covers a wide range of topics fundamental to calculating integrals on computer systems and discusses both the theoretical and computational aspects of numerical and symbolic methods. It includes extensive sections on one- and multidimensional integration formulas, like polynomial, number-theoretic, and pseudorandom formulas, and deals with issues concerning the construction of numerical integration algorithms.
A Panorama Of Discrepancy Theory
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Author : William Chen
language : en
Publisher: Springer
Release Date : 2014-10-07
A Panorama Of Discrepancy Theory written by William Chen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-07 with Mathematics categories.
This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory. Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling and is currently located at the crossroads of number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. This book presents an invitation to researchers and students to explore the different methods and is meant to motivate interdisciplinary research.
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.