A low-rank approach to the computation of path integrals

JOURNAL OF COMPUTATIONAL PHYSICS

卷:305

Article

Litsarev, Mikhail S.¹  Oseledets, Ivan V.^1,2 

[1] Skolkovo Innovat Ctr, Skolkovo Inst Sci & Technol, Moscow 143026, Russia

[2] Russian Acad Sci, Inst Numer Math, Moscow 119333, Russia

关键词: Low-rank approximation;    Feynman-Kac formula;    Path integral;    Multidimensional integration;    Skeleton approximation;    Convolution;   

DOI  :  10.1016/j.jcp.2015.11.009

来源: Elsevier

【 摘 要 】

We present a method for solving the reaction-diffusion equation with general potential in free space. It is based on the approximation of the Feynman-Kac 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(nrMlogM + nr(2)M) flops and requires O(Mr) floating-point numbers in memory, where n is the dimension of the integral, r << n, and M is the mesh size in one dimension. The presented technique can be generalized to the higher-order diffusion processes. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free