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Lattice Methods for Multiple Integration (Oxford Science Publications) [Hardcover]

I. H. Sloan (Author), S. Joe (Author)

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Product details

Hardcover: 252 pages
Publisher: Clarendon Press (13 Oct 1994)
Language English
ISBN-10: 0198534728
ISBN-13: 978-0198534723
Product Dimensions: 23.5 x 16.2 x 1.9 cm
Amazon Bestsellers Rank: 1,598,178 in Books (See Top 100 in Books)
- #48 in Books > Science & Nature > Mathematics > Calculus & Mathematical Analysis > Calculus of Variations
- #52 in Books > Science & Nature > Mathematics > Numerical Analysis

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Review

"I can recommend this book to everyone who wants or needs to know more about computing multivariate integrals. This book gives a very good overview of the current state-of-the-art lattice rules, and it is very readable."--Bulletin of the American Mathematical Society
"This book is devoted to the numerical multiple integration based on lattice rules, generalizing the rectangle rule for an interval."--Mathematical Reviews

Product Description

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 avery efficent manner. the book also provides a fast track for readers wanting to move rapidly to using methods in practical calculations. It concludes with extensive numerical test which compare lattice methods with other methods, such as the Monte Carlo.

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First Sentence
This book is concerned with a class of methods, called lattice methods, for the numerical evaluation of multiple integrals. Read the first page

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Amazon.com: 1 review

1 of 1 people found the following review helpful

Readable, practical, theoretical 15 Jun 2002

By J. Cook - Published on Amazon.com

Format:Hardcover

This is a surprizingly readable account of a tricky subject. The author provides a good theoretical background, but realizes that some readers will want implement lattice rules without studying all the underlying theory, and organizes the book accordingly.

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