Backward Stability of the Schur Canonical Form
In the present paper, we show the backward stability of the Schur decomposition for a given matrix under small perturbation.
math.CA↗
arXiv subjects
Vadim Olshevsky
Publications and source records attributed to Vadim Olshevsky.
Gohberg-Kaashoek Numbers and Forward Stability of the Schur Canonical Form
In the present paper we complete the stability of Schur decomposition depending on the Jordan structure of the perturbation, started in \cite{MNO}.
math.CA↗
A Fast Algorithm for the Inversion of Quasiseparable Vandermonde-like Matrices
The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasiseparable, semiseparable and well-free Vandermonde-like matrices having $\mathcal{O}(n^2)$ complexity. To do so we identify structures of displacement operators in terms of generators and the recurrence relations(2-term and 3-term) between the columns of the basis transformation matrices for quasiseparable, semiseparable and well-free polynomials. Finally we present an $\mathcal{O}(n^2)$ algorithm to compute the inversion of quasiseparable Vandermonde-like matrices.
math.NA↗