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TW 504
Raf Vandebril, Marc Van Barel, Nicola Mastronardi
A rational QR-iteration
Abstract
In this manuscript a new type of QR-iteration will be presented. Each step of this new iteration consists of two substeps, first an RQ-factorization of the initial matrix A - κ I = RQ will be computed, followed by a QR-factorization of the matrix (A - σ I)QH. Applying the unitary similarity transformation defined by the QR-factorization of the transformed matrix (A - σ I)QH, will yield interesting convergence properties. It will be shown that the convergence behavior is related to a subspace iteration based on a rational function in A namely (A - σ I)(A - κ I)-1. Convergence properties of this new iteration will be investigated and examples will be presented, illustrating the effectiveness of this approach with respect to some specific classes of matrices.
report.pdf (510K) / mailto: R. Vandebril