A low-rank approach to the computation of path integrals

Mikhail S. Litsarev, Ivan V. Oseledets

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    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+nr2M) 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.

    Original languageEnglish
    Pages (from-to)557-574
    Number of pages18
    JournalJournal of Computational Physics
    Volume305
    DOIs
    Publication statusPublished - 15 Jan 2016

    Keywords

    • Convolution
    • Feynman-Kac formula
    • Low-rank approximation
    • Multidimensional integration
    • Path integral
    • Skeleton approximation

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