A Perturbative Analysis of the Reduction into Diagonal-plus-semiseparable Form of Symmetric Matrices.

It is known that any symmetric matrix can be transformed by an explicitly computable orthogonal transformation into diagonal-plus-semiseparable form, with prescribed diagonal term. In this paper, we present perturbation bounds for such transformations, under the condition that the diagonal term is close to (part of) the spectrum of the given matrix. As an application, we provide new iterative schemes for the simultaneous refinement of the eigenvalues of a symmetric matrix, having quadratic convergence. [ABSTRACT FROM AUTHOR]