Year: 2026
Type: preprint
Abstract: The rectangular multiparameter eigenvalue problem (rMEP) is a recently introduced form of an eigenvalue problem, in which we are looking for the combinations of parameters where the multivariate rectangular matrix loses full column rank. Existing numerical methods for rMEPs typically require substantial memory and are not suitable for problems with a large number of eigenvalues. We propose a novel numerical approach based on the homotopy method that has low memory requirements and can compute all eigenvalues of an rMEP. Moreover, the homotopy method is naturally parallelizable, providing a simple and efficient way to accelerate computations. An implementation, together with a collection of test examples, is available in a public repository.
Source: arXiv (Cornell University)
Authors: Plestenjak, Bor, Vermeersch, Christof
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221814717