Solving a class of multivariate integration problems via Laplace techniques

Jean B. Lasserre, and Eduardo S. Zeron. "Solving a class of multivariate integration problems via Laplace techniques." Applicationes Mathematicae 28.4 (2001): 391-405. <http://eudml.org/doc/279101>.

@article{JeanB2001,
abstract = {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.},
author = {Jean B. Lasserre, Eduardo S. Zeron},
journal = {Applicationes Mathematicae},
keywords = {multivariate integration; Laplace transform; closed form expression; convex polyhedron; ellipsoid; generalized polynomial; exponential of a linear form; trigonometric polynomials; exponential of a quadratic form},
language = {eng},
number = {4},
pages = {391-405},
title = {Solving a class of multivariate integration problems via Laplace techniques},
url = {http://eudml.org/doc/279101},
volume = {28},
year = {2001},
}

TY - JOUR
AU - Jean B. Lasserre
AU - Eduardo S. Zeron
TI - Solving a class of multivariate integration problems via Laplace techniques
JO - Applicationes Mathematicae
PY - 2001
VL - 28
IS - 4
SP - 391
EP - 405
AB - 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.
LA - eng
KW - multivariate integration; Laplace transform; closed form expression; convex polyhedron; ellipsoid; generalized polynomial; exponential of a linear form; trigonometric polynomials; exponential of a quadratic form
UR - http://eudml.org/doc/279101
ER -