Greedy algorithms for high-dimensional eigenvalue problems

TL;DR

This paper introduces two novel greedy algorithms for efficiently computing the lowest eigenvalues and eigenvectors in high-dimensional problems, with proven convergence and demonstrated effectiveness on practical numerical examples.

Contribution

The paper proposes new greedy algorithms for high-dimensional eigenvalue problems, including convergence analysis and comparison with existing methods.

Findings

Algorithms converge under certain conditions.

Numerical tests show competitive performance.

Effective in computing buckling modes of microstructured plates.

Abstract

In this article, we present two new greedy algorithms for the computation of the lowest eigenvalue (and an associated eigenvector) of a high-dimensional eigenvalue problem, and prove some convergence results for these algorithms and their orthogonalized versions. The performance of our algorithms is illustrated on numerical test cases (including the computation of the buckling modes of a microstructured plate), and compared with that of another greedy algorithm for eigenvalue problems introduced by Ammar and Chinesta.