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.
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