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Numerical solution of the eigenvalue problem for Hermitian Toeplitz-like matrices

Ng, Michael K; Trench, William F

Description

An iterative method based on displacement structure is proposed for computing eigenvalues and eigenvectors of a class of Hermitian Toeplitz-like matrices which includes matrices of the form T*T where T is arbitrary Toeplitz matrix, Toeplitz-block matrices and block-Toeplitz matrices. The method obtains a specific individual eigenvalue (i.e., the i-th smallest, where i is a specified integer in [1, 2,...,n]) of an n x n matrix at a computational cost of O(n2) operations. An associated...[Show more]

dc.contributor.authorNg, Michael K
dc.contributor.authorTrench, William F
dc.date.accessioned2003-07-08
dc.date.accessioned2004-05-19T12:32:59Z
dc.date.accessioned2011-01-05T08:37:49Z
dc.date.available2004-05-19T12:32:59Z
dc.date.available2011-01-05T08:37:49Z
dc.date.created1997
dc.identifier.urihttp://hdl.handle.net/1885/40750
dc.identifier.urihttp://digitalcollections.anu.edu.au/handle/1885/40750
dc.description.abstractAn iterative method based on displacement structure is proposed for computing eigenvalues and eigenvectors of a class of Hermitian Toeplitz-like matrices which includes matrices of the form T*T where T is arbitrary Toeplitz matrix, Toeplitz-block matrices and block-Toeplitz matrices. The method obtains a specific individual eigenvalue (i.e., the i-th smallest, where i is a specified integer in [1, 2,...,n]) of an n x n matrix at a computational cost of O(n2) operations. An associated eigenvector is obtained as a byproduct. The method is more efficient than general purpose methods such as the QR algorithm for obtaining a small number (compared to n) of eigenvalues. Moreover, since the computation of each eigenvalue is independent of the computation of all other eigenvalues, the method is highly parallelizable. Numerical results illustrate the effectiveness of the method.
dc.format.extent247168 bytes
dc.format.extent356 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/octet-stream
dc.language.isoen_AU
dc.subjectToeplitz matrix
dc.subjectdisplacement structure
dc.subjectToeplitz-like matrix
dc.subjecteigenvalue
dc.subjecteigenvector
dc.subjectroot-finding
dc.titleNumerical solution of the eigenvalue problem for Hermitian Toeplitz-like matrices
dc.typeWorking/Technical Paper
local.description.refereedno
local.identifier.citationmonthjul
local.identifier.citationyear1997
local.identifier.eprintid1579
local.rights.ispublishedyes
dc.date.issued1997
local.contributor.affiliationANU
local.contributor.affiliationDepartment of Computer Science, FEIT
local.citationTR-CS-97-14
CollectionsANU Research Publications

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