NDLI: Some Fast Algorithms for Sequentially Semiseparable Representations

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Dewilde, P. White, D. Pals, T. Sun, X. Chandrasekaran, S. Gu, M. van der Veen, A. J.
Copyright Year	2005
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.
Starting Page	341
Ending Page	364
Page Count	24
File Format	PDF
ISSN	08954798
DOI	10.1137/S0895479802405884
e-ISSN	10957162
Journal	SIAM Journal on Matrix Analysis and Applications (SJMAEL)
Issue Number	2
Volume Number	27
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-31
Access Restriction	Subscribed
Subject Keyword	time-varying systems spectral methods backward stability scattering theory Direct methods for linear systems and matrix inversion fast multipole method integral equations semiseparable matrices Other matrix algorithms method of moments Overdetermined systems, pseudoinverses fast direct solver Moore--Penrose inverses
Content Type	Text
Resource Type	Article
Subject	Analysis

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