The unitary completion and QR iterations for a class of structured matrices

Bini, D.; Eidelman, Y.; Gemignani, L.; Gohberg, I.

doi:10.1090/S0025-5718-07-02004-2

The unitary completion and QR iterations for a class of structured matrices
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by D. A. Bini, Y. Eidelman, L. Gemignani and I. Gohberg;

Math. Comp. 77 (2008), 353-378

DOI: https://doi.org/10.1090/S0025-5718-07-02004-2

Published electronically: June 22, 2007

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Abstract:

We consider the problem of completion of a matrix with a specified lower triangular part to a unitary matrix. In this paper we obtain the necessary and sufficient conditions of existence of a unitary completion without any additional constraints and give a general formula for this completion. The paper is mainly focused on matrices with the specified lower triangular part of a special form. For such a specified part the unitary completion is a structured matrix, and we derive in this paper the formulas for its structure. Next we apply the unitary completion method to the solution of the eigenvalue problem for a class of structured matrices via structured QR iterations.

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