Subject: Book: LATTICE METHODS FOR MULTIPLE INTEGRATION

From: Jan Labanowski <[email-masked]>
Date: Wed, 23 Nov 1994 11:38:20 -0500

For people who do grids, it may be of great interest:

Ian H. Sloan and Stephen Joe
Oxford University Press, New York and Oxford 1994.
ISBN 0-19-853472-8
250 pages, 60 line figures
Price:  $US55   

Orders from OUP Customer Services, 2001 Evans Road, Cary, NC 27513,
phone 800-451-7556 fax 919-677-1303. Postage and packaging $2.50.

This book is the first devoted to lattice methods, a recently developed
method for the evaluation of multiple integrals in many variables, which
arise in quantum physics and chemistry, statistical mechanics, Bayesian
statistics, and many other fields.

The book begins with a review of existing methods, before presenting lattice
rules in a thorough self-contained manner, with numerous illustrations and
examples.  Group theory and number theory enter the story, but the treatment 
is such that no prior knowledge of these subjects is required.

Both the theory and practical implementation are covered.  An algorithm is
presented along with tables not available elsewhere, allowing the practical
evaluation of multiple integrals in up to at least 12 variables.  Most
importantly, the algorithm produces a very efficient estimate of the error.

The book provides a fast track for readers wanting to move rapidly to using
lattice mathods in practical calculations.  It concludes with the results
of extensive numerical comparisons with other methods, such as the 
Monte Carlo method.

Jan Labanowski
[email-masked]
(No, I am not a contributor to this book and have no commercial or
career interest).