Lattice Rules for Multiple Integration and Discrepance
Author: Harald Niederreiter
Publisher:
Published: 1989
Total Pages: 19
ISBN-13:
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Author: Harald Niederreiter
Publisher:
Published: 1989
Total Pages: 19
ISBN-13:
DOWNLOAD EBOOKAuthor: Vasile Sinescu
Publisher:
Published: 2008
Total Pages: 154
ISBN-13:
DOWNLOAD EBOOKAuthor: I. H. Sloan
Publisher: Oxford University Press
Published: 1994
Total Pages: 256
ISBN-13: 9780198534723
DOWNLOAD EBOOKThis 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
Published: 2022-08-24
Total Pages: 584
ISBN-13: 3031099516
DOWNLOAD EBOOKLattice 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: Michael Drmota
Publisher: Springer
Published: 2006-11-14
Total Pages: 517
ISBN-13: 354068333X
DOWNLOAD EBOOKThe 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.
Author:
Publisher:
Published: 1990
Total Pages: 9
ISBN-13:
DOWNLOAD EBOOKAuthor: Arnold R. Krommer
Publisher: SIAM
Published: 1998-01-01
Total Pages: 464
ISBN-13: 9781611971460
DOWNLOAD EBOOKThis 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.
Author: Josef Dick
Publisher:
Published: 2004
Total Pages: 116
ISBN-13:
DOWNLOAD EBOOKAuthor: William Chen
Publisher: Springer
Published: 2014-10-07
Total Pages: 708
ISBN-13: 3319046969
DOWNLOAD EBOOKThis 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.
Author: Arnold R. Krommer
Publisher: Springer Science & Business Media
Published: 1994-09-28
Total Pages: 366
ISBN-13: 9783540584100
DOWNLOAD EBOOKThe 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.