, Volume 70, Issue 4, pp 1934-1943

Computation of exponential integrals

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Abstract

Let P⊂ ℝ d be a convex polyhedron and f: ℝ d→ℝ a linear function. One studies the computational complexity of the integral ∫pexp f(xdx. It is shown that these integrals satisfy nontrivial algebraic relations, which makes possible the construction of polynomial algorithms for certain polyhedra. Examples are given of the application of exponential integrals to the calculation of volume and nonlinear programming.

Translated from Zapiski Nauchnykh Seminarov Leningradksogo Otdeleniya Matematicheskogo Instituta im. V. A. Skeklova AN SSSR, Vol. 192, pp. 149–162, 1991.