Computing pseudospectra of polynomial eigenvalue problems: direct approach vs linearization

Zhengsheng Wang, Yuanjun Li, Chuntao Liu

Abstract


Pseudospectra of polynomial eigenvalue problems (PEPs) have been investigated in recent years. In this paper, we firstly investigate the grid method, linearization method for pseudospectra of PEPs. Then, we explore a method for computing the pseudospectra of large PEPs, which is so called generalized projection method that projects to reduce the size of the problem directly using the generalized Arnoldi iteration. At last, numerical experiments and comparisons are given to illustrate the efficiency of generalized projection method and the different sensitivity of these methods.


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How to Cite this Article:

Zhengsheng Wang, Yuanjun Li, Chuntao Liu, Computing pseudospectra of polynomial eigenvalue problems: direct approach vs linearization, Journal of Mathematical and Computational Science, Vol 2, No 4 (2012), 1101-1115

Copyright © 2012 Zhengsheng Wang, Yuanjun Li, Chuntao Liu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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