00000cab a22000003a 4500 UP-99796217608727444 Buklod 20231007234725.0 m |o d | ta 090225s xx d | ||r ||||| || (iLib)UPD-00075999500 DENGII eng Lasserre, Jean B. A Laplace transform algorithm for the volume of a convex polytope. pp. 1126-1140 We provide two algorithms for computing the volume of the convex polytope Ω : = {x ∈ ℝn+ | Ax ≤ b}, for A, ∈ ℝm×n, b ∈ ℝn. The computational complexity of both algorithms is essentially described by nm, which makes them especially attractive for large n and relatively small m, when the other methods with O(mn) complexity fail. The methodology, which differs from previous existing methods, uses a Laplace transform technique that is well suited to the half-space representation of Ω. Theory of computation. Analysis of algorithms and problem complexity. Numerical algorithms and problems. Computation of transforms (e.g., fast Fourier transform). Mathematics of computing. Numerical analysis. Numerical algorithms. Algorithms. Journal of the ACM 48, 6 (2001). FO UPD DENG-II Article