%0 Journal Article %1 citeulike:2760994 %A Bai, Zhaojun %A Demmel, James W. %C Philadelphia, PA, USA %D 1993 %I Society for Industrial and Applied Mathematics %J SIAM Journal on Scientific Computing %K 68w01-algorithms-general 15a18-eigenvalues-singular-values-and-eigenvectors 15a22-matrix-pencils %N 6 %P 1464--1486 %R 10.1137/0914085 %T Computing the Generalized Singular Value Decomposition %U http://dx.doi.org/10.1137/0914085 %V 14 %X A variation of Paige's algorithm is presented for computing the generalized singular value decomposition (GSVD) of two matrices A and B. There are two innovations. The first is a new preprocessing step which reduces A and B to upper triangular forms satisfying certain rank conditions. The second is a new \$2 2\$ triangular GSVD algorithm, which constitutes the inner loop of Paige's algorithm. Proofs of stability and high accuracy of the \$2 2\$ GSVD algorithm are presented and are demonstrated using examples on which all previous algorithms fail.

@article{citeulike:2760994, abstract = {{A variation of Paige's algorithm is presented for computing the generalized singular value decomposition (GSVD) of two matrices A and B. There are two innovations. The first is a new preprocessing step which reduces A and B to upper triangular forms satisfying certain rank conditions. The second is a new \$2 \times 2\$ triangular GSVD algorithm, which constitutes the inner loop of Paige's algorithm. Proofs of stability and high accuracy of the \$2 \times 2\$ GSVD algorithm are presented and are demonstrated using examples on which all previous algorithms fail.}}, added-at = {2017-06-29T07:13:07.000+0200}, address = {Philadelphia, PA, USA}, author = {Bai, Zhaojun and Demmel, James W.}, biburl = {https://www.bibsonomy.org/bibtex/2bca402c32b1d0d0a8ae8d74a09299d1c/gdmcbain}, citeulike-article-id = {2760994}, citeulike-attachment-1 = {bai_93_computing_1026941.pdf; /pdf/user/gdmcbain/article/2760994/1026941/bai_93_computing_1026941.pdf; 2cf267966d15672d8b65774f62bc61e83a77e77f}, citeulike-linkout-0 = {http://portal.acm.org/citation.cfm?id=163239}, citeulike-linkout-1 = {http://dx.doi.org/10.1137/0914085}, doi = {10.1137/0914085}, file = {bai_93_computing_1026941.pdf}, interhash = {8fa67c4d6183ebfdaa56e08aa27e46d6}, intrahash = {bca402c32b1d0d0a8ae8d74a09299d1c}, issn = {1064-8275}, journal = {SIAM Journal on Scientific Computing}, keywords = {68w01-algorithms-general 15a18-eigenvalues-singular-values-and-eigenvectors 15a22-matrix-pencils}, month = nov, number = 6, pages = {1464--1486}, posted-at = {2015-07-22 05:44:40}, priority = {2}, publisher = {Society for Industrial and Applied Mathematics}, timestamp = {2020-01-31T05:49:40.000+0100}, title = {{Computing the Generalized Singular Value Decomposition}}, url = {http://dx.doi.org/10.1137/0914085}, volume = 14, year = 1993 }