English

A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system

Numerical Analysis 2016-01-19 v1 Exactly Solvable and Integrable Systems

Abstract

A generalized eigenvalue algorithm for tridiagonal matrix pencils is presented. The algorithm appears as the time evolution equation of a nonautonomous discrete integrable system associated with a polynomial sequence which has some orthogonality on the support set of the zeros of the characteristic polynomial for a tridiagonal matrix pencil. The convergence of the algorithm is discussed by using the solution to the initial value problem for the corresponding discrete integrable system.

Keywords

Cite

@article{arxiv.1303.1035,
  title  = {A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system},
  author = {Kazuki Maeda and Satoshi Tsujimoto},
  journal= {arXiv preprint arXiv:1303.1035},
  year   = {2016}
}

Comments

24 pages, 2 figures, 3 tables

R2 v1 2026-06-21T23:36:54.695Z