A low-rank approach to the computation of path integrals

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 $\mathcal{O}(nrM\log M+n{r}^{2}M)$ flops and requires $\mathcal{O}(Mr)$ floating-point numbers in memory, where $n$ is the dimension of the integral, $r\ll n$, and $M$ is the mesh size in one dimension. The presented technique can be generalized to the higher-order diffusion processes.

References in corpus (2)

• Tensor Numerical Methods in Quantum Chemistry: from Hartree-Fock Energy to Excited States
• Fast low-rank approximations of multidimensional integrals in ion-atomic collisions modelling

Cited by in corpus (1)

• Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives