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TW 380
Marc Van Barel, Ellen Van Camp, Nicola Mastronardi
Orthogonal similarity transformation into semiseparable matrices of semiseparability rank k
Abstract
Very recently, an algorithm, which reduces any symmetric matrix into a semiseparable one of semiseparability rank 1 by similar orthogonality transformations, has been proposed by Vandebril, Van Barel and Mastronardi. Partial execution of this algorithm computes a semiseparable matrix whose eigenvalues are the Ritz-values obtained by the Lanczos' process applied to the original matrix. Also a kind of nested subspace iteration is performed at each step.
In this paper, we generalize the above results and propose an algorithm to reduce any symmetric matrix into a similar block-semiseparable one of semiseparability rank k, with k ∈ N, by orthogonal similarity transformations. Also in this case partial execution of the algorithm computes a block-semiseparable matrix whose eigenvalues are the Ritz-values obtained by the block-Lanczos' process with k starting vectors, applied to the original matrix. Subspace iteration is performed at each step as well.
report.pdf (565K) / mailto: M. Van Barel