A Parallel Approach for Computing Complex Eigenvalue Problems

Yao-Lin JIANG  Richard M. M. CHEN  Zu-Lan HUANG  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.10   pp.2000-2008
Publication Date: 2000/10/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Numerical Analysis and Optimization
complex eigenvalue problems,  optimization,  dynamic equations,  waveform relaxation,  parallel processing,  

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In this paper we study general complex eigenvalue problems in engineering fields. The eigenvalue problems can be transformed into the associated problems for solving large systems of nonlinear ordinary differential equations (dynamic equations) by optimization techniques. The known waveform relaxation method in circuit simulation can then be successfully applied to compute the resulting dynamic equations. The approach reported here, which is implemented on a message passing multi-processor system, can determine all eigenvalues and their eigenvectors for general complex matrices without any restriction on the matrices. The numerical results are provided to confirm the theoretical analysis.