Computing the generalized singular value decomposition.(English)Zbl 0621.65030

The author describes an algorithm for computing the generalized singular value decomposition (GSVD) of any two matrices having the same number of columns. The GSVD of matrices A(m$$\times n)$$, B(p$$\times n)$$ consists in finding unitary matrices U, V, Q such that $$U^ HAQ=\sum_ AR$$, $$V^ HBQ=\sum_ BR$$, where $$\sum_ A(m\times n)=diag(\alpha_ 1,\alpha_ 2,...)\geq 0,$$ and $$\sum_ B(p\times n)=diag(\beta_ 1,\beta_ 2,...)\geq 0,$$ and R is upper triangular. The iterative algorithm is based on Kogbetliantz’s method for computing the singular value decomposition of matrices. A description of the theoretical behaviour of the algorithm as well as numerical examples of its application are given. Some remarks on a systolic array implementation are included.
Reviewer: T.Reginska

MSC:

 65F15 Numerical computation of eigenvalues and eigenvectors of matrices 15A18 Eigenvalues, singular values, and eigenvectors 15A23 Factorization of matrices
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