Lattice Methods for Multiple Integration

Hardcover | October 1, 1990

byI. H. Sloan, S. Joe

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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 methodsare 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 estimatein 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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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 methodsare an effective tool when the number of int...

I. H. Sloan is at University of New South Wales. S. Joe is at University of Waikato.

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Format:HardcoverDimensions:250 pages, 9.21 × 6.14 × 0.79 inPublished:October 1, 1990Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198534728

ISBN - 13:9780198534723

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Table of Contents

PrefaceIntroduction1. Lattice rules2. Lattice rules as multiple sums3. Rank-1 rules - the method of good lattice points4. Lattice rules of higher rank - a first look5. Maximal rank lattice rules6. Intermediate rank lattice rules7. Lattice rules for nonperiodic integrands8. Lattice rules - other topics9. Practical implementation of lattice rules10. Comparisons with other methodsAppendicesReferencesIndex

Editorial Reviews

`This nice book gives a thorough coverage of the numerical integration of high dimensional functions by means of lattice rules.....................I found the book very readable, and busy readers are well advised by the authors how to spend best their time with the book'Monatshefte fur Mathematik Vol. 124 1997