Journal Article10.1137/090777542
Solving Rational Eigenvalue Problems via Linearization
Yangfeng Su,Zhaojun Bai +1 more
TL;DR: It is shown that solving a class of rational eigen value problems is just as convenient and efficient as solving linear eigenvalue problems.
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Abstract: The rational eigenvalue problem is an emerging class of nonlinear eigenvalue problems arising from a variety of physical applications. In this paper, we propose a linearization-based method to solve the rational eigenvalue problem. The proposed method converts the rational eigenvalue problem into a well-studied linear eigenvalue problem, and meanwhile, exploits and preserves the structure and properties of the original rational eigenvalue problem. For example, the low-rank property leads to a trimmed linearization. We show that solving a class of rational eigenvalue problems is just as convenient and efficient as solving linear eigenvalue problems.
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Citations
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