Papers › Automatic rational approximation and linearization of nonlinear eigenvalue problems
Automatic rational approximation and linearization of nonlinear eigenvalue problems
Pieter Lietaert, Javier Pérez, Bart Vandereycken, Karl Meerbergen
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We present a method for solving nonlinear eigenvalue problems using rational approximation. The method uses the AAA method by Nakatsukasa, S\`{e}te, and Trefethen to approximate the nonlinear eigenvalue problem by a rational eigenvalue problem and is embedded in the state space representation of a rational polynomial by Su and Bai. The advantage of the method, compared to related techniques such as NLEIGS and infinite Arnoldi, is the efficient computation by an automatic procedure. In addition, a set-valued approach is developed that allows building a low degree rational approximation of a nonlinear eigenvalue problem. The method perfectly fits the framework of the Compact rational Krylov methods (CORK and TS-CORK), allowing to efficiently solve large scale nonlinear eigenvalue problems. Numerical examples show that the presented framework is competitive with NLEIGS and usually produces smaller linearizations with the same accuracy but with less effort for the user.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections