%0 Journal Article %1 1327974 %A Willems, Paul R. %A Lang, Bruno %A Vo\¨mel, Christof %C Philadelphia, PA, USA %D 2006 %I Society for Industrial and Applied Mathematics %J SIAM J. Matrix Anal. Appl. %K algorithm computing multiple robust svd %N 4 %P 907--926 %R http://dx.doi.org/10.1137/050628301 %T Computing the Bidiagonal SVD Using Multiple Relatively Robust Representations %U http://portal.acm.org/citation.cfm?id=1327974 %V 28 %X We describe the design and implementation of a new algorithm for computing the singular value decomposition (SVD) of a real bidiagonal matrix. This algorithm uses ideas developed by Grosser and Lang that extend Parlett’s and Dhillon’s multiple relatively robust representations (MRRR) algorithm for the tridiagonal symmetric eigenproblem. One key feature of our new implementation is that $k$ singular triplets can be computed using only $O(nk)$ storage units and floating point operations, where $n$ is the dimension of the matrix. The algorithm will be made available as routine xBDSCR in the upcoming new release of the LAPACK library.

@article{1327974, abstract = {We describe the design and implementation of a new algorithm for computing the singular value decomposition (SVD) of a real bidiagonal matrix. This algorithm uses ideas developed by Grosser and Lang that extend Parlett’s and Dhillon’s multiple relatively robust representations (MRRR) algorithm for the tridiagonal symmetric eigenproblem. One key feature of our new implementation is that $k$ singular triplets can be computed using only $\mathcal{O}(nk)$ storage units and floating point operations, where $n$ is the dimension of the matrix. The algorithm will be made available as routine xBDSCR in the upcoming new release of the LAPACK library.}, added-at = {2009-08-07T07:08:25.000+0200}, address = {Philadelphia, PA, USA}, author = {Willems, Paul R. and Lang, Bruno and Vo\¨mel, Christof}, biburl = {https://www.bibsonomy.org/bibtex/20ec95a4bca5e56d732f39620efddb921/folke}, description = {Computing the Bidiagonal SVD Using Multiple Relatively Robust Representations}, doi = {http://dx.doi.org/10.1137/050628301}, interhash = {52b9a6c03334206eba8bb52f15f0e738}, intrahash = {0ec95a4bca5e56d732f39620efddb921}, issn = {0895-4798}, journal = {SIAM J. Matrix Anal. Appl.}, keywords = {algorithm computing multiple robust svd}, number = 4, pages = {907--926}, publisher = {Society for Industrial and Applied Mathematics}, timestamp = {2009-08-07T07:08:25.000+0200}, title = {Computing the Bidiagonal SVD Using Multiple Relatively Robust Representations}, url = {http://portal.acm.org/citation.cfm?id=1327974}, volume = 28, year = 2006 }