SIAM J. on Matrix Analysis and Applications

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Print: 0895-4798
Electronic: 1095-7162
Coden: SJMAEL

The SIAM Journal on Matrix Analysis and Applications publishes research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.

Featured Article

Stable Computation of the CS Decomposition: Simultaneous Bidiagonalization

Since its discovery in 1977, the CS decomposition (CSD) has resisted computation, even though it is a sibling of the well-understood eigenvalue and singular value decompositions. Several algorithms have been developed for the reduced 2-by-1 form of the decomposition, but none have been extended to the complete 2-by-2 form of the decomposition in Stewart's original paper. In this article, we present an algorithm for simultaneously bidiagonalizing the four blocks of a unitary matrix partitioned into a 2-by-2 block structure. This serves as the first, direct phase of a two-stage algorithm for the CSD, much as Golub–Kahan–Reinsch bidiagonalization serves as the first stage in computing the singular value decomposition. Backward stability is proved.

SIAM. J. Matrix Anal. & Appl. 33, pp. 1-21