The modified bordering method to evaluate eigenvalues and eigenvectors of normal matrices |
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Authors: | M. Morandi Cecchi E. Di Nardo |
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Affiliation: | (1) Dipartimento di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, I-35131 Padova, Italy;(2) Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, Monte S. Angelo, I-80126 Napoli, Italy |
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Abstract: | A bordering procedure is here proposed to evaluate the eigensystem of hermitian matrices, and more in general of normal matrices, when the spectral decomposition is known of then–1×n–1 principal minor. The procedure is also applicable to special real and nonsymmetric matrices here named quasi-symmetric. The computational cost to write the characteristic polynomial isO(n2), using a new set of recursive formulas. A modified Brent algorithm is used to find the roots of the polynomial. The eigenvectors are evaluated in a direct way with a computational cost ofO(n2) for each one. Some numerical considerations indicate where numerical difficulties may occur. Numerical results are given comparing this method with the Givens-Householder one. |
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