A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix

The known formula [ ] ( ) 1 1 / Tr N N λ = A , where A is an n n × Hermitian matrix, 1 λ is its dominant eigenvalue and N is a sufficiently large positive integer, is given the modification ( ) 1 1 / Tr N N λ = A . This modification is conjectured to apply to any n n × matrices, whether Hermitian or...

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Main Authors:	Gonzalez, Emmanuel A., Estalilla, Aliento V.
Format:	text
Published:	Animo Repository 2007
Subjects:	Hermitian operators Eigenvalues Theory and Algorithms
Online Access:	https://animorepository.dlsu.edu.ph/faculty_research/9832
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Institution:	De La Salle University

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spelling	oai:animorepository.dlsu.edu.ph:faculty_research-120602023-10-16T00:45:04Z A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix Gonzalez, Emmanuel A. Estalilla, Aliento V. The known formula [ ] ( ) 1 1 / Tr N N λ = A , where A is an n n × Hermitian matrix, 1 λ is its dominant eigenvalue and N is a sufficiently large positive integer, is given the modification ( ) 1 1 / Tr N N λ = A . This modification is conjectured to apply to any n n × matrices, whether Hermitian or not and is converted into an algorithm for obtaining the modulus of the dominant eigenvalue of A . A heuristic basis for the correctness of the latter formula is given. Several numerical examples with graphical representations of their convergences are given, including an unusual case where ongoing steps give alternately the exact value and the successive approximations of the dominant eigenvalue. 2007-03-01T08:00:00Z text https://animorepository.dlsu.edu.ph/faculty_research/9832 Faculty Research Work Animo Repository Hermitian operators Eigenvalues Theory and Algorithms
institution	De La Salle University
building	De La Salle University Library
continent	Asia
country	Philippines Philippines
content_provider	De La Salle University Library
collection	DLSU Institutional Repository
topic	Hermitian operators Eigenvalues Theory and Algorithms
spellingShingle	Hermitian operators Eigenvalues Theory and Algorithms Gonzalez, Emmanuel A. Estalilla, Aliento V. A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix
description	The known formula [ ] ( ) 1 1 / Tr N N λ = A , where A is an n n × Hermitian matrix, 1 λ is its dominant eigenvalue and N is a sufficiently large positive integer, is given the modification ( ) 1 1 / Tr N N λ = A . This modification is conjectured to apply to any n n × matrices, whether Hermitian or not and is converted into an algorithm for obtaining the modulus of the dominant eigenvalue of A . A heuristic basis for the correctness of the latter formula is given. Several numerical examples with graphical representations of their convergences are given, including an unusual case where ongoing steps give alternately the exact value and the successive approximations of the dominant eigenvalue.
format	text
author	Gonzalez, Emmanuel A. Estalilla, Aliento V.
author_facet	Gonzalez, Emmanuel A. Estalilla, Aliento V.
author_sort	Gonzalez, Emmanuel A.
title	A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix
title_short	A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix
title_full	A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix
title_fullStr	A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix
title_full_unstemmed	A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix
title_sort	conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix
publisher	Animo Repository
publishDate	2007
url	https://animorepository.dlsu.edu.ph/faculty_research/9832
_version_	1781418116006281216

A conjectured algorithm for determining the modulus of the dominant eigenvalue of an arbitrary square matrix

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