Subspace method for multiparameter-eigenvalue problems based on tensor-train representations

In this article, we solve m-parameter eigenvalue problems (mEPs), with m any natural number by representing the problem using tensor-trains (TTs) and designing a method based on this format. mEPs typically arise when separation of variables is applied to separable boundary value problems. Often, methods for solving mEP are restricted to m=3, due to the fact that, to the best of our knowledge, no available solvers exist for m>3 and reasonable size of the involved matrices. In this article, we prove that computing the eigenvalues of a mEP can be recast into computing the eigenvalues of TT-operators. We adapted the algorithm in(9) for symmetric eigenvalue problems in TT-format to an algorithm for solving generic mEPs. This leads to a subspace method whose subspace dimension does not depend on m, in contrast to other subspace methods for mEPs. This allows us to tackle mEPs with m>3 and reasonable size of the matrices. We provide theoretical results and report numerical experiments. The MATLAB code is publicly available.

Jaar van publicatie:2022

Trefwoorden:A1 Journal article

Toegankelijkheid:Open