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Generalized qd algorithm for block band matrices

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Abstract

The generalized qd algorithm for block band matrices is an extension of the block qd algorithm applied to a block tridiagonal matrix. This algorithm is applied to a positive definite symmetric block band matrix. The result concerning the behavior of the eigenvalues of the first and the last diagonal block of the matrix containing the entries q (k) which was obtained in the tridiagonal case is still valid for positive definite symmetric block band matrices. The eigenvalues of the first block constitute strictly increasing sequences and those of the last block constitute strictly decreasing sequences. The theorem of convergence, given in Draux and Sadik (Appl Numer Math 60:1300–1308, 2010), also remains valid in this more general case.

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Authors and Affiliations

  1. Département de Génie Mathématique, INSA de Rouen, Campus de Saint-Étienne-du-Rouvray, Avenue de l’université, BP 8, 76801, Saint-Étienne-du-Rouvray Cedex, France

    André Draux & Mohamed Sadik

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  1. André Draux
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  2. Mohamed Sadik
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Correspondence to André Draux.

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Draux, A., Sadik, M. Generalized qd algorithm for block band matrices. Numer Algor 61, 377–396 (2012). https://doi.org/10.1007/s11075-012-9538-1

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  • DOI: https://doi.org/10.1007/s11075-012-9538-1

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