Book: LATTICE METHODS FOR MULTIPLE INTEGRATION

[Jan Labanowski <jkl # - at - # ccl.net>]

 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
 jkl # - at - # ccl.net
 (No, I am not a contributor to this book and have no commercial or
 career interest).