Trace inverse algorithms for the general eigenvalue problem

Mohammed A. Hasan; Ali A. Hasan

Trace inverse algorithms for the general eigenvalue problem

Electrical Engineering

Research output: Contribution to journal › Conference article › peer-review

Abstract

Computation of matrix eigenvalues forms one of the basic problems in numerical linear algebra and is of fundamental importance in applied science and engineering. In this paper, "Trace Inverse Algorithms" in rational and radical forms are introduced. These algorithms are applied for computing the eigenvalues of rank one modification, bordered matrices, and the Hessenberg eigenvalue problem. Using this approach a sample of extremum eigenvalue finders are developed. These methods are iterative and can be designed to have convergence of any prescribed order. Generalization to the general nonlinear eigenvalue problem is also presented.

Original language	English (US)
Pages (from-to)	2111-2116
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	2
State	Published - 2002
Event	41st IEEE Conference on Decision and Control - Las Vegas, NV, United States Duration: Dec 10 2002 → Dec 13 2002

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title = "Trace inverse algorithms for the general eigenvalue problem",

abstract = "Computation of matrix eigenvalues forms one of the basic problems in numerical linear algebra and is of fundamental importance in applied science and engineering. In this paper, {"}Trace Inverse Algorithms{"} in rational and radical forms are introduced. These algorithms are applied for computing the eigenvalues of rank one modification, bordered matrices, and the Hessenberg eigenvalue problem. Using this approach a sample of extremum eigenvalue finders are developed. These methods are iterative and can be designed to have convergence of any prescribed order. Generalization to the general nonlinear eigenvalue problem is also presented.",

author = "Hasan, {Mohammed A.} and Hasan, {Ali A.}",

year = "2002",

language = "English (US)",

volume = "2",

pages = "2111--2116",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0191-2216",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "41st IEEE Conference on Decision and Control ; Conference date: 10-12-2002 Through 13-12-2002",

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T1 - Trace inverse algorithms for the general eigenvalue problem

AU - Hasan, Mohammed A.

AU - Hasan, Ali A.

PY - 2002

Y1 - 2002

N2 - Computation of matrix eigenvalues forms one of the basic problems in numerical linear algebra and is of fundamental importance in applied science and engineering. In this paper, "Trace Inverse Algorithms" in rational and radical forms are introduced. These algorithms are applied for computing the eigenvalues of rank one modification, bordered matrices, and the Hessenberg eigenvalue problem. Using this approach a sample of extremum eigenvalue finders are developed. These methods are iterative and can be designed to have convergence of any prescribed order. Generalization to the general nonlinear eigenvalue problem is also presented.

AB - Computation of matrix eigenvalues forms one of the basic problems in numerical linear algebra and is of fundamental importance in applied science and engineering. In this paper, "Trace Inverse Algorithms" in rational and radical forms are introduced. These algorithms are applied for computing the eigenvalues of rank one modification, bordered matrices, and the Hessenberg eigenvalue problem. Using this approach a sample of extremum eigenvalue finders are developed. These methods are iterative and can be designed to have convergence of any prescribed order. Generalization to the general nonlinear eigenvalue problem is also presented.

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M3 - Conference article

AN - SCOPUS:0036990356

SN - 0191-2216

VL - 2

SP - 2111

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JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - 41st IEEE Conference on Decision and Control

Y2 - 10 December 2002 through 13 December 2002

ER -

Trace inverse algorithms for the general eigenvalue problem

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