A low-rank approach to the computation of path integrals
We present a method for solving the reactiondiffusion equation with general potential in free space. It is based on the approximation of the FeynmanKac formula by a sequence of convolutions on sequentially diminishing grids. For computation of the convolutions we propose a fast algorithm based on the low-rank approximation of the Hankel matrices. The algorithm has complexity of O(nrMlog?M+nr2M) O ( n r M log ? M + n r 2 M ) flops and requires O(Mr) O ( M r ) floating-point numbers in memory, where n  is the dimension of the integral, r?n r ? n , and M is the mesh size in one dimension. The presented technique can be generalized to the higher-order diffusion processes.
path integral feynmankac formula convolution low-rank approximation multidimensional integration skeleton approximation