Some Fast Algorithms for Sequentially Semiseparable Representations

Authors:
S. Chandrasekaran;P. Dewilde;M. Gu;T. Pals;X. Sun;A.-J. vander Veen;D. White
Affiliations:
-;-;-;-;-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2005

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Abstract

An extended sequentially semiseparable (SSS) representation derived from time-varying system theory is used to capture, on the one hand, the low-rank of the off-diagonal blocks of a matrix for the purposes of efficient computations and, on the other, to provide for sufficient descriptive richness to allow for backward stability in the computations. We present (i) a fast algorithm (linear in the number of equations) to solve least squares problems in which the coefficient matrix is in SSS form, (ii) a fast algorithm to find the SSS form of X such that AX=B, where A and B are in SSS form, and (iii) a fast model reduction technique to improve the SSS form.