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)
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)
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)
We derive new estimates of the spectral dichotomy for matrices and matrix pencils which are based upon estimates of the restrictions of Green functions associated with the spectrum dichotomy problem onto the stable and unstable invariant subspaces and estimates of angles between these subspaces. De nouvelles estimations pour la dichotomie spectrale R esum e(More)