NDLI: Convergence of the Dominant Pole Algorithm and Rayleigh Quotient Iteration

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Rommes, Joost Sleijpen, Gerard L. G.
Copyright Year	2008
Abstract	The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. In this paper, two methods for the computation of the dominant poles of a large scale transfer function are studied: two-sided Rayleigh quotient iteration (RQI) and the dominant pole algorithm (DPA). First, a local convergence analysis of DPA will be given, and the local convergence neighborhoods of the dominant poles will be characterized for both methods. Second, theoretical and numerical results will be presented that indicate that for DPA the basins of attraction of the dominant pole are larger than those for two-sided RQI. The price for the better global convergence is only a few additional iterations, due to the asymptotically quadratic rate of convergence of DPA, against the cubic rate of two-sided RQI.
Starting Page	346
Ending Page	363
Page Count	18
File Format	PDF
ISSN	08954798
DOI	10.1137/060671401
e-ISSN	10957162
Journal	SIAM Journal on Matrix Analysis and Applications (SJMAEL)
Issue Number	1
Volume Number	30
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2008-03-19
Access Restriction	Subscribed
Subject Keyword	subspace accelerated Newton method transfer function eigenvalues modal model reduction dominant poles eigenvectors two-sided Rayleigh quotient iteration dominant pole algorithm rate of convergence Eigenvalues, eigenvectors
Content Type	Text
Resource Type	Article
Subject	Analysis

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