Solving Rational Eigenvalue Problems via Linearization

Rational eigenvalue problems (REPs) are an emerging class of nonlinear eigenvalue problems that arise from a variety of physical applications. In this paper, we propose a linearization-based method to solve the REPs. Similar to the linearization techniques for the polynomial eigenvalue problems, the proposed method converts the REPs into well-studied linear eigenvalue problems (LEPs), and meanwhile, exploits and preserves the structure and property of the REPs. For example, the low-rank property as encountered in practical applications leads a trimmed linearization, that is, only small increase of the size of LEP. Under mild assumptions, we show that the problem of solving a REP is just as convenient and efficient as the problem of solving a LEP of slightly larger size.

• Type: Journal
• Year: 2011
• Where: SIAMMAX
• Authors: Yangfeng Su, Zhaojun Bai
• Keywords: Eigenvalue Problems, Nonlinear Eigenvalue Problems, Rational Eigenvalue Problems, SIAMMAX 2011