Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form

Authors:
Dario Fasino;Nicola Mastronardi;Marc Van Barel
Affiliations:
Dipartimento Di Matematica E Informatica, Universitá Degli Studi Di Udine, Udine, Italy;Istituto Per Le Applicazioni Del Calcolo "M. Picone", Consiglio Nazionale Delle Ricerche, Sez. Bari, Bari, Italy;Department of Computer Science, Katholieke Universiteit Leuven, Celestijnen-Laan, Leuven, Belgium
Venue:
Contemporary mathematics
Year:
2001

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Abstract

New algorithms to reduce a diagonal plus a symmetric semiseparable matrix to a symmetric tridiagonal one and an algorithm to reduce a diagonal plus an unsymmetric semiseparable matrix to a bidiagonal one are considered. The algorithms are fast and stable, requiring a computational cost of O(N2), where N is the order of the considered matrix.