Lattice Methods For Multiple Integration

Author : I. H. Sloan,S. Joe
Publisher : Oxford University Press
Page : 256 pages
File Size : 50,8 Mb
Release : 1994
Category : Mathematics
ISBN : 0198534728

Get Book

Lattice Methods for Multiple Integration by I. H. Sloan,S. Joe Pdf

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,Frances Y. Kuo,Henryk Woźniakowski
Publisher : Springer
Page : 1309 pages
File Size : 49,5 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9783319724560

Get Book

Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan by Josef Dick,Frances Y. Kuo,Henryk Woźniakowski Pdf

This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

Author : Josef Dick,Peter Kritzer,Friedrich Pillichshammer
Publisher : Springer Nature
Page : 584 pages
File Size : 48,8 Mb
Release : 2022-08-24
Category : Mathematics
ISBN : 9783031099519

Get Book

Lattice Rules by Josef Dick,Peter Kritzer,Friedrich Pillichshammer Pdf

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
Page : 247 pages
File Size : 44,5 Mb
Release : 1992-01-01
Category : Mathematics
ISBN : 1611970083

Get Book

Random Number Generation and Quasi-Monte Carlo Methods by Harald Niederreiter Pdf

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 : Stefka Fidanova
Publisher : Springer Nature
Page : 388 pages
File Size : 47,5 Mb
Release : 2022-09-16
Category : Technology & Engineering
ISBN : 9783031068393

Get Book

Recent Advances in Computational Optimization by Stefka Fidanova Pdf

This book presents recent advances in computational optimization. The book includes important real problems like modeling of physical processes, parameter settings for controlling different processes, transportation problems, machine scheduling, air pollution modeling, solving multiple integrals and systems of differential and integral equations which describe real processes, solving engineering and financial problems. It shows how to develop algorithms for them based on new intelligent methods like evolutionary computations, ant colony optimization, constrain programming Monte Carlo method and others. This research demonstrates how some real-world problems arising in engineering, economics and other domains can be formulated as optimization problems.

Author : Pierre L' Ecuyer,Art B. Owen
Publisher : Springer Science & Business Media
Page : 669 pages
File Size : 41,9 Mb
Release : 2010-01-14
Category : Mathematics
ISBN : 9783642041075

Get Book

Monte Carlo and Quasi-Monte Carlo Methods 2008 by Pierre L' Ecuyer,Art B. Owen Pdf

This book represents the refereed proceedings of the Eighth International Conference on Monte Carlo (MC)and Quasi-Monte Carlo (QMC) Methods in Scientific Computing, held in Montreal (Canada) in July 2008. It covers the latest theoretical developments as well as important applications of these methods in different areas. It contains two tutorials, eight invited articles, and 32 carefully selected articles based on the 135 contributed presentations made at the conference. This conference is a major event in Monte Carlo methods and is the premiere event for quasi-Monte Carlo and its combination with Monte Carlo. This series of proceedings volumes is the primary outlet for quasi-Monte Carlo research.

Author : Dana Simian,Laura Florentina Stoica
Publisher : Springer Nature
Page : 348 pages
File Size : 54,8 Mb
Release : 2023-02-25
Category : Computers
ISBN : 9783031270345

Get Book

Modelling and Development of Intelligent Systems by Dana Simian,Laura Florentina Stoica Pdf

This book constitutes the refereed proceedings of the 8th International Conference on Modelling and Development of Intelligent Systems, MDIS 2022, held in Sibiu, Romania, during October 28–30, 2022. The 21 papers included in this book were carefully reviewed and selected from 48 submissions. They were organized in the following topical sections as follows: intelligent systems for decision support; machine learning; mathematical models for development of intelligent systems; and modelling and optimization of dynamic systems.

Author : Leszek Plaskota,Henryk Woźniakowski
Publisher : Springer Science & Business Media
Page : 721 pages
File Size : 44,6 Mb
Release : 2012-08-23
Category : Mathematics
ISBN : 9783642274404

Get Book

Monte Carlo and Quasi-Monte Carlo Methods 2010 by Leszek Plaskota,Henryk Woźniakowski Pdf

This book represents the refereed proceedings of the Ninth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at the University of Warsaw (Poland) in August 2010. These biennial conferences are major events for Monte Carlo and the premiere event for quasi-Monte Carlo research. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. The reader will be provided with information on latest developments in these very active areas. The book is an excellent reference for theoreticians and practitioners interested in solving high-dimensional computational problems arising, in particular, in finance and statistics.

Author : HÄMMERLIN,BRASS
Publisher : Birkhäuser
Page : 338 pages
File Size : 42,6 Mb
Release : 2013-12-14
Category : Science
ISBN : 9783034863988

Get Book

Numerical Integration III by HÄMMERLIN,BRASS Pdf

Author : Christiane Lemieux
Publisher : Springer Science & Business Media
Page : 373 pages
File Size : 50,8 Mb
Release : 2009-04-03
Category : Mathematics
ISBN : 9780387781655

Get Book

Monte Carlo and Quasi-Monte Carlo Sampling by Christiane Lemieux Pdf

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 : John H. Conway,Neil J.A. Sloane
Publisher : Springer Science & Business Media
Page : 690 pages
File Size : 54,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475720167

Get Book

Sphere Packings, Lattices and Groups by John H. Conway,Neil J.A. Sloane Pdf

The main themes. This book is mainly concerned with the problem of packing spheres in Euclidean space of dimensions 1,2,3,4,5, . . . . Given a large number of equal spheres, what is the most efficient (or densest) way to pack them together? We also study several closely related problems: the kissing number problem, which asks how many spheres can be arranged so that they all touch one central sphere of the same size; the covering problem, which asks for the least dense way to cover n-dimensional space with equal overlapping spheres; and the quantizing problem, important for applications to analog-to-digital conversion (or data compression), which asks how to place points in space so that the average second moment of their Voronoi cells is as small as possible. Attacks on these problems usually arrange the spheres so their centers form a lattice. Lattices are described by quadratic forms, and we study the classification of quadratic forms. Most of the book is devoted to these five problems. The miraculous enters: the E 8 and Leech lattices. When we investigate those problems, some fantastic things happen! There are two sphere packings, one in eight dimensions, the E 8 lattice, and one in twenty-four dimensions, the Leech lattice A , which are unexpectedly good and very 24 symmetrical packings, and have a number of remarkable and mysterious properties, not all of which are completely understood even today.

Author : Daniel Zwillinger
Publisher : CRC Press
Page : 384 pages
File Size : 53,8 Mb
Release : 1992-11-02
Category : Mathematics
ISBN : 9781439865842

Get Book

The Handbook of Integration by Daniel Zwillinger Pdf

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

Author : Alexander Keller,Stefan Heinrich,Harald Niederreiter
Publisher : Springer Science & Business Media
Page : 684 pages
File Size : 42,8 Mb
Release : 2007-12-30
Category : Mathematics
ISBN : 9783540744962

Get Book

Monte Carlo and Quasi-Monte Carlo Methods 2006 by Alexander Keller,Stefan Heinrich,Harald Niederreiter Pdf

This book presents the refereed proceedings of the Seventh International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing, held in Ulm, Germany, in August 2006. The proceedings include carefully selected papers on many aspects of Monte Carlo and quasi-Monte Carlo methods and their applications. They also provide information on current research in these very active areas.

Author : Christoph W. Ueberhuber
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642591181

Get Book

Numerical Computation 1 by Christoph W. Ueberhuber Pdf

This book deals with various aspects of scientific numerical computing. No at tempt was made to be complete or encyclopedic. The successful solution of a numerical problem has many facets and consequently involves different fields of computer science. Computer numerics- as opposed to computer algebra- is thus based on applied mathematics, numerical analysis and numerical computation as well as on certain areas of computer science such as computer architecture and operating systems. Applied Mathemalies I I I Numerical Analysis Analysis, Algebra I I Numerical Computation Symbolic Computation I Operating Systems Computer Hardware Each chapter begins with sample situations taken from specific fields of appli cation. Abstract and general formulations of mathematical problems are then presented. Following this abstract level, a general discussion about principles and methods for the numerical solution of mathematical problems is presented. Relevant algorithms are developed and their efficiency and the accuracy of their results is assessed. It is then explained as to how they can be obtained in the form of numerical software. The reader is presented with various ways of applying the general methods and principles to particular classes of problems and approaches to extracting practically useful solutions with appropriately chosen numerical software are developed. Potential difficulties and obstacles are examined, and ways of avoiding them are discussed. The volume and diversity of all the available numerical software is tremendous.

Author : Harald Niederreiter
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 54,6 Mb
Release : 2011-06-28
Category : Mathematics
ISBN : 9783642187438

Get Book

Monte Carlo and Quasi-Monte Carlo Methods 2002 by Harald Niederreiter Pdf

This book represents the refereed proceedings of the Fifth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing which was held at the National University of Singapore in the year 2002. An important feature are invited surveys of the state of the art in key areas such as multidimensional numerical integration, low-discrepancy point sets, computational complexity, finance, and other applications of Monte Carlo and quasi-Monte Carlo methods. These proceedings also include carefully selected contributed papers on all aspects of Monte Carlo and quasi-Monte Carlo methods. The reader will be informed about current research in this very active area.