Lattice Methods for Multiple Integration [Hardcover]

Lattice methods were recently developed to handle the multiple integrals that occur in quantum chemistry, physics, statistical mechanics, Bayesian statistics, and numerous other fields.Lattice Methods for Multiple Integrationprovides an outstanding introduction to the subject, offering numerous examples and detailed, practical descriptions of how each method can be applied to a wide range of situations. Thorough and self-contained, the book includes a user-friendly overview of lattice theory and introduces an important new algorithm--along with tables unavailable elsewhere--that both allows for the practical evaluation of multiple integrals in many variables and efficiently produces an error estimate. The book concludes with extensive numerical tests which compare lattice methods to other methods, such as the Monte Carlo.

Preface
Introduction
1. Lattice Rules
2. Lattice Rules as Multiple Sums
3. Rank-1 Rules--The Method of Good Lattice Points
4. Lattice Rules of Higher Rank--A First Look
5. Maximal Rank Lattice Rules
6. Intermediate Rank Lattice Rules
7. Lattice Rules for Nonperiodic Integrands
8. Lattice Rules--Other Topics
9. Practical Implementation of Lattice Rules
10. Comparisons with Other Methods
Appendices
References
Index

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