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- Alexander N. Malyshev
- Numerische Mathematik
- 1999

- Alexander N. Malyshev, Miloud Sadkane
- Numerical Lin. Alg. with Applic.
- 2014

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)

- Alexander N. Malyshev
- SIAM J. Matrix Analysis Applications
- 2003

- Alexander N. Malyshev
- Computing
- 2000

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)

- Alexander N. Malyshev
- SIAM J. Matrix Analysis Applications
- 2006

We prove that the 2-distance from an n n matrix A to the matrices that have a multiple eigenvalue is equal to max 0 2n?1

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)

K.V. Fernando developed an efficient approach for computation of an eigenvector of a tridiagonal matrix corresponding to an approximate eigenvalue. We supplement Fernando’s method with deflation procedures by Givens rotations. These deflations can be used in the Lanczos process and instead of the inverse iteration.

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)