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Towards a Generalized Singular Value Decomposition
C. C. Paige and M. A. Saunders
SIAM Journal on Numerical Analysis
Vol. 18, No. 3 (Jun., 1981), pp. 398-405
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2156862
Page Count: 8
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We suggest a form for, and give a constructive derivation of, the generalized singular value decomposition of any two matrices having the same number of columns. We outline its desirable characteristics and compare it to an earlier suggestion by Van Loan [SIAM J. Numer. Anal., 13 (1976), pp. 76-83]. The present form largely follows from the work of Van Loan, but is slightly more general and computationally more amenable than that in the paper cited. We also prove a useful extension of a theorem of Stewart [SIAM Rev. 19 (1977), pp. 634-662] on unitary decompositions of submatrices of a unitary matrix.
SIAM Journal on Numerical Analysis © 1981 Society for Industrial and Applied Mathematics