An inexact Newton-Krylov method for stochastic eigenvalue problems

TL;DR

This paper introduces a low-rank inexact Newton method that efficiently solves high-dimensional stochastic eigenvalue problems by exploiting tensor product structures, demonstrated through numerical experiments.

Contribution

The paper develops a novel globalized low-rank inexact Newton method tailored for stochastic eigenvalue problems, leveraging tensor product structures for improved efficiency.

Findings

Effective solver demonstrated through numerical experiments

Reduces computational complexity for high-dimensional problems

Exploits tensor product structure for efficiency

Abstract

This paper aims at the efficient numerical solution of stochastic eigenvalue problems. Such problems often lead to prohibitively high dimensional systems with tensor product structure when discretized with the stochastic Galerkin method. Here, we exploit this inherent tensor product structure to develop a globalized low-rank inexact Newton method with which we tackle the stochastic eigenproblem. We illustrate the effectiveness of our solver with numerical experiments.