Alexander N. Malyshev

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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 subspaces corresponding to the eigenvalues(More)
Peters and Wilkinson [2] 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 [1]. The present note fills this gap. Gauss–Jordan elimination is backward stable for matrices diagonally dominant by rows and not for those diagonally dominant by columns. In either case it is(More)
This paper presents some practical and guaranteed ways of studying the discrete-time/ continuous-time stability quality of large sparse matrices. The methods use projection techniques for computing an invariant subspace associated with a few outermost eigenvalues (those with largest real parts for the continuous-time case and with largest magnitudes in the(More)