Year: 2025
Type: preprint
Abstract: The rectangular multiparameter eigenvalue problem (RMEP) involves rectangular coefficient matrices (usually with more rows than columns) and may potentially have no solution in its original form. A minimal perturbation framework is proposed to defines approximate solutions. Computationally, two particular scenarios are considered: computing one approximate eigen-tuple or a complete set of approximate eigen-tuples. For computing one approximate eigen-tuple, an alternating iterative scheme with proven convergence is devised, while for a complete set of approximate eigen-tuples, the framework leads to a standard MEP (RMEP with square coefficient matrices) for numerical solutions. The proposed approach is validated on RMEPs from discretizing the multiparameter Sturm-Liouville equation and the Helmholtz equations by the least-squares spectral method.
Source: arXiv (Cornell University)
Authors: Han, Shanheng, Zhang, Lei-Hong, Li, Ren-Cang
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415192098
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