Abstract
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.
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© 2007 Birkhäuser Verlag Basel/Switzerland
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Fasino, D. (2007). A Perturbative Analysis of the Reduction into Diagonal-plus-semiseparable Form of Symmetric Matrices. In: Ball, J.A., Eidelman, Y., Helton, J.W., Olshevsky, V., Rovnyak, J. (eds) Recent Advances in Matrix and Operator Theory. Operator Theory: Advances and Applications, vol 179. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8539-2_9
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DOI: https://doi.org/10.1007/978-3-7643-8539-2_9
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