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

### 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.author Ng, Michael K Trench, William F 2003-07-08 2004-05-19T12:32:59Z 2011-01-05T08:37:49Z 2004-05-19T12:32:59Z 2011-01-05T08:37:49Z 1997 http://hdl.handle.net/1885/40750 http://digitalcollections.anu.edu.au/handle/1885/40750 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 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. 247168 bytes 356 bytes application/pdf application/octet-stream en_AU Toeplitz matrix displacement structure Toeplitz-like matrix eigenvalue eigenvector root-finding Numerical solution of the eigenvalue problem for Hermitian Toeplitz-like matrices Working/Technical Paper no jul 1997 1579 yes 1997 ANU Department of Computer Science, FEIT TR-CS-97-14 ANU Research Publications