dhw@iti.org (David H. West) (05/10/91)
I saw (but can't find) a report that someone has discovered a way to hybridize Monte Carlo and Gaussian Numerical Integration: you specify a tolerance e and a number of dimensions k, and the method computes an integer N and a set of N points (and presumably weights) in the unit k-dimensional hypercube such that in some probabilistic sense function values at those points allow the integral of the function to be estimated with precision better than e for "almost all" functions, AND the behavior of N with k is much better than the e^-k that Monte Carlo gives. Can anyone point me to this work? Please email. thanks, -David West dhw@iti.org
kuszewsk@euler.biology.yale.edu (John Kuszewski) (05/13/91)
Check out "Average case complexity of Multivariate integration" by Henryk Wozniakowski in Bull. Amer. Math. Soc. 24, p. 185 (Jan. 1991) and "Theory and applications of information-based complexity" by H. Wozniakowski and J. F. Traub to appear in 1990 Lectures in Complex Systems, SFI Studies in the Sciences of Complexity, Lect. Vol. III (L. Nadel and D. Stein, eds.), Addison-Wesley, 1991 If you write to Dr. Traub's secretary, Kerny McLaughlin, at kerny@cs.columbi.edu and ask really nicely, she'll send you preprints of both. Hope this helps. --- John Kuszewski kuszewsk@euler.biology.yale.edu