A rational QR-iteration
نویسندگان
چکیده
In this manuscript a new type of QR-iteration will be presented. Each step of this new iteration consists of two substeps. In the explicit version, first an RQ-factorization of the initial matrix A−κI = RQ will be computed, followed by a QR-factorization of the matrix (A−σI)QH . Applying the unitary similarity transformation defined by the QR-factorization of the transformed matrix (A−σI)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 − σI)(A − κI). 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
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