We consider the problem of calculating a closed form expression for the integral of a real-valued function f:ℝⁿ → ℝ on a set S. We specialize to the particular cases when S is a convex polyhedron or an ellipsoid, and the function f is either a generalized polynomial, an exponential of a linear form (including trigonometric polynomials) or an exponential of a quadratic form. Laplace transform techniques allow us to obtain either a closed form expression, or a series representation that can be handled numerically. Finally, a methodology is proposed for multivariate functions f which have a (multidimensional) Laplace transform.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am28-4-2,
author = {Jean B. Lasserre and Eduardo S. Zeron},
title = {Solving a class of multivariate integration problems via Laplace techniques},
journal = {Applicationes Mathematicae},
volume = {28},
year = {2001},
pages = {391-405},
zbl = {1008.65016},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-4-2}
}
Jean B. Lasserre; Eduardo S. Zeron. Solving a class of multivariate integration problems via Laplace techniques. Applicationes Mathematicae, Tome 28 (2001) pp. 391-405. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-4-2/