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Computation of exponential integrals. (Russian. English summary) Zbl 0753.65018

The author considers integrals of the form \(\int_ P\exp\{\langle c,x\rangle\}\rho(x)dx\), \(c\in \mathbb{R}^ n\), \(\rho: \mathbb{R}^ n\to \mathbb{R}\) being a polynomial density, where \(P\) is a convex full-dimensional polytope; their computational complexity is studied. He establishes some non-trivial algebraic relations which allow him to design polynomial-time algorithms for some polytopes. There are applications to computation of the volume of a polytope and to a problem of nonlinear programming.

MSC:

65D32 Numerical quadrature and cubature formulas
65Y20 Complexity and performance of numerical algorithms
68Q25 Analysis of algorithms and problem complexity
52B12 Special polytopes (linear programming, centrally symmetric, etc.)
52B55 Computational aspects related to convexity
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