A generalized eigenvalue algorithm for tridiagonal matrix pencils based on a nonautonomous discrete integrable system
arXiv:1303.1035 · doi:10.1016/j.cam.2015.12.032
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.
24 pages, 2 figures, 3 tables
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