Year: 2023
Type: article
Abstract: We describe a strategy for solving nonlinear eigenproblems numerically. Our approach is based on the approximation of a vector‐valued function, defined as solution of a non‐homogeneous version of the eigenproblem. This approximation step is carried out via the minimal rational interpolation method. Notably, an adaptive sampling approach is employed: the expensive data needed for the approximation is gathered at locations that are optimally chosen by following a greedy error indicator. This allows the algorithm to employ computational resources only where where “most of the information” on not‐yet‐approximated eigenvalues can be found. Then, through a post‐processing of the surrogate, the sought‐after eigenvalues and eigenvectors are recovered. Numerical examples are used to showcase the effectiveness of the method.
Source: PAMM
Author: Davide Pradovera
Institution: University of Vienna
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4360879534