A low-rank approach to the computation of path integrals

被引：5
作者：
Litsarev, Mikhail S. [1 ]
Oseledets, Ivan V. [1 ,2 ]
机构：
[1] Skolkovo Innovat Ctr, Skolkovo Inst Sci & Technol, Moscow 143026, Russia
[2] Russian Acad Sci, Inst Numer Math, Moscow 119333, Russia
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2016年 / 305卷
基金：
俄罗斯科学基金会;
关键词：
Low-rank approximation; Feynman-Kac formula; Path integral; Multidimensional integration; Skeleton approximation; Convolution; MULTIDIMENSIONAL NONLOCAL OPERATORS; KRONECKER-PRODUCT APPROXIMATION; TENSOR APPROXIMATION; EQUATION; DIMENSIONALITY; REPRESENTATION; DECOMPOSITION; ALGORITHMS; MATRICES;
D O I：
10.1016/j.jcp.2015.11.009
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
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.
引用
收藏
页码：557 / 574
页数：18
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