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  A STUDY OF THE HR AND EXTENDED HR METHODS FOR THE STANDARD EIGENVALUE PROBLEM

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by Petter Wiberg
http://www.cerfacs.fr/algor/reports/TR_PA_97_33.ps.gz
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Abstract:

Abstract. The QR method is a very efficient method for computing the spectrum of Hermitian tridiagonal matrices since the tridiagonal form is preserved over the iterations. For non-Hermitian tridiagonal matrices the QR method destroys the tridiagonal form. In this report we study two methods, the HR and the XHR methods, that preserve tridiagonal form for pseudo-Hermitian matrices. We also report results from numerical experiments using the algorithms and try to point out short comings and possible strategies for future

Citations

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1 Numerics of Gram-Schmidt Orthogonalization – Bjork - 1994
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