From: spellucci@mathematik.tu-darmstadt.de (Peter Spellucci) Subject: Re: multiple integration Date: 14 Jan 2000 17:17:20 GMT Newsgroups: sci.math.num-analysis Summary: [missing] In article <387E3B90.518DA310@namtar.qub.ac.uk>, b9628959 writes: |> i would be graetful if some one could help me on genaral information on |> the above topic |> claires_baby@hotmail.com |> stroud: approximate calculation of multiple integral, prentice hall 1971 very good source on genral principles and known formulae see also the following information which i have in my annotations: In a recent paper ("Faster Evaluation of Multidimensional Integrals" by A. Papageorgiou and J. F. Traub, Computers in Physics, 11(6), 1997, 574-578), a high-dimensional model problem proposed by the physicist B.D. Keister was tested. This problem is isotropic. findings: quasi-Monte Carlo converged as 1/n while Monte Carlo converged as 1/sqrt(n). Quasi-Monte Carlo was also greatly superior to several quadrature rules tested by Keister. You may obtain the paper as well as papers reporting test :results from mathematical finance at www.cs.columbia.edu/~traub ------------------------------------------------------------- keast@mscs.dal.ca (Pat Keast) writes: > ... > J.N. Lyness and Ronald Cools: A survey of Numerical Cubature over Triangles, > and references in there. There is also a paper by Cools and Rabinowitz which > you can get from Cools' web page. Cools is probably a very good source. > > The Lyness-Cools paper is at > http://www-fp.mcs.anl.gov/division/publications/preprints.htm > > Cools' e-mail is Ronald.Cools@cs.kuleuven.ac.be and his web page is at > > http://www.cs.kuleuven.ac.be/~ronald/index.html > ... Here you can find html tables of cubature formulae over a variety of domains together with references. It's great ! ------------------------------------------------------------- The next choice could be the Number theoretic algorithms, based on Korobov points, as found in Comp. Phys. Comm. 14, 299 (1978) Comp. Phys. Comm. 31, 1 (1984) hope this helps peter