A Laplace transform algorithm for the volume of a convex polytope

We provide two algorithms for computing the volume of the convex polytope Omega := {x is an element of R-+(n) \ Ax less than or equal to b}, for A is an element of R-mxn, b is an element of R-n. The computational complexity of both algorithms is essentially described by n(m), which makes them especially attractive for large n and relatively small in, when the other methods with O(m(n)) 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 Omega.