特征向量非线性的轮廓积分

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2023-10-30 DOI:10.1137/22m1497985

Rob Claes, Karl Meerbergen, Simon Telen

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引用次数: 0

摘要

求解具有特征向量非线性(PEPv)的多项式特征值问题是一个有趣的计算挑战，超出了非线性特征值问题的成熟方法的范围。我们提出了这些方法的自然推广，这导致了计算复平面紧致区域中PEPv的所有特征值的轮廓积分方法。我们的方法可用于求解任何适当的多项式或有理函数方程的一般系统。

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Contour Integration for Eigenvector Nonlinearities

Solving polynomial eigenvalue problems with eigenvector nonlinearities (PEPv) is an interesting computational challenge, outside the reach of the well-developed methods for nonlinear eigenvalue problems. We present a natural generalization of these methods which leads to a contour integration approach for computing all eigenvalues of a PEPv in a compact region of the complex plane. Our methods can be used to solve any suitably generic system of polynomial or rational function equations.

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.