Barvinok, A. I. Computation of exponential integrals. (Russian. English summary) Zbl 0753.65018 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 192, 149-162 (1991). 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. Reviewer: L.P.Lebedev (Rostov-na-Donu) Cited in 1 ReviewCited in 3 Documents 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 Keywords:exponential integrals; polytope; computational complexity; polynomial- time algorithms; volume PDFBibTeX XMLCite \textit{A. I. Barvinok}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 192, 149--162 (1991; Zbl 0753.65018) Full Text: EuDML