@misc{Zha, author = {Zha, Hongyuan}, title = {A Numerical Algorithm for Computing the Restricted Singular Value Decomposition of Matrix Triplets.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-194}, number = {SC-89-01}, abstract = {This paper presents a numerical algorithm for computing the restricted singular value decomposition of matrix triplets (RSVD). It is shown that one can use unitary transformations to separate the regular part from a general matrix triplet. After preprocessing on the regular part, one obtains a matrix triplet consisting of three upper triangular matrices of the same dimensions. The RSVD of this special matrix triplet is computed using the implicit Kogbetliantz technique. The algorithm is well suited for parallel computation. {\bf Keywords:} Restricted singular values, matrix triplets, unitary transformations, implicit Kogbetliantz technique.}, language = {en} } @misc{Zha, author = {Zha, Hongyuan}, title = {Restricted Singular Value Decomposition of Matrix Triplets.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-205}, number = {SC-89-02}, abstract = {In this paper we introduce the concept of restricted singular values (RSV's) of matrix triplets. A theorem concerning the RSV's of a general matrix triplet \$ (A,B,C) \$, where \$ A \in C^{m\times n} \$, \$B\in C^{m\times p} \$ and \$ C\in C^{q\times n} \$, which is called restricted singular value decomposition (RSVD) of matrix triplets, is derived. This result generalizes the wellknown SVD, GSVD and the recently proposed product induced SVD (PSVD). Connection of RSV's with the problem of determination of matrix rank under restricted perturbation is also discussed. {\bf Keywords:} Matrix rank, singular values, generalized singular values, product induced singular values, restricted singular values, matrix decompositions.}, language = {en} }