Alexander N. Malyshev

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We discuss two spectral dichotomy techniques: one for computing an invariant subspace of a nonsymmetric matrix associated with the eigenvalues inside and outside a given parabola. Another for computing a right deeating subspace of a regular matrix pencil associated with the eigenvalues inside and outside a given ellipse. The techniques use matrices of order(More)
Peters and Wilkinson 4] state that \it is well known that Gauss-Jordan is stable" for a diagonally dominant matrix, but a proof does not seem to have been published 3]. The present note lls this gap. Gauss-Jordan elimination is backward stable for matrices diagonally dominant by rows and not backward stable for matrices diagonally dominant by columns. In(More)
SUMMARY A fast algorithm for solving systems of linear equations with banded Toeplitz matrices is studied. An important step in the algorithm is a novel method for the spectral factorization of the generating function associated with the Toeplitz matrix. The spectral factorization is extracted from the right deflating sub-spaces corresponding to the(More)