%0 Generic %D 2018 %T Bidiagonal SVD Computation via an Associated Tridiagonal Eigenproblem %A Osni Marques %A James Demmel %A Paulo B. Vasconcelos %X In this paper, we present an algorithm for the singular value decomposition (SVD) of a bidiagonal matrix by means of the eigenpairs of an associated symmetric tridiagonal matrix. The algorithm is particularly suited for the computation of a subset of singular values and corresponding vectors. We focus on a sequential version of the algorithm, and discuss special cases and implementation details. We use a large set of bidiagonal matrices to assess the accuracy of the implementation in single and double precision, as well as to identify potential shortcomings. We show that the algorithm can be up to three orders of magnitude faster than existing algorithms, which are limited to the computation of a full SVD. We also show time comparisons of an implementation that uses the strategy discussed in the paper as a building block for the computation of the SVD of general matrices. %B LAPACK Working Note %I University of Tennessee %8 2018-04 %G eng %0 Conference Proceedings %B PARA 2008, 9th International Workshop on State-of-the-Art in Scientific and Parallel Computing %D 2008 %T Interior State Computation of Nano Structures %A Andrew Canning %A Jack Dongarra %A Julien Langou %A Osni Marques %A Stanimire Tomov %A Christof Voemel %A Lin-Wang Wang %B PARA 2008, 9th International Workshop on State-of-the-Art in Scientific and Parallel Computing %C Trondheim, Norway %8 2008-05 %G eng %0 Journal Article %J Journal of Computational Physics %D 2008 %T State-of-the-Art Eigensolvers for Electronic Structure Calculations of Large Scale Nano-Systems %A Christof Voemel %A Stanimire Tomov %A Osni Marques %A Andrew Canning %A Lin-Wang Wang %A Jack Dongarra %B Journal of Computational Physics %V 227 %P 7113-7124 %8 2008-01 %G eng %0 Journal Article %J Journal of Computational Physics %D 2007 %T The Use of Bulk States to Accelerate the Band Edge State Calculation of a Semiconductor Quantum Dot %A Christof Voemel %A Stanimire Tomov %A Lin-Wang Wang %A Osni Marques %A Jack Dongarra %B Journal of Computational Physics %V 223 %P 774-782 %8 2007-00 %G eng %0 Conference Proceedings %B IEEE/ACM Proceedings of HPCNano SC06 (to appear) %D 2006 %T Performance evaluation of eigensolvers in nano-structure computations %A Andrew Canning %A Jack Dongarra %A Julien Langou %A Osni Marques %A Stanimire Tomov %A Christof Voemel %A Lin-Wang Wang %K doe-nano %B IEEE/ACM Proceedings of HPCNano SC06 (to appear) %8 2006-01 %G eng %0 Journal Article %J J. Phys.: Conf. Ser. 46 %D 2006 %T Predicting the electronic properties of 3D, million-atom semiconductor nanostructure architectures %A Alex Zunger %A Alberto Franceschetti %A Gabriel Bester %A Wesley B. Jones %A Kwiseon Kim %A Peter A. Graf %A Lin-Wang Wang %A Andrew Canning %A Osni Marques %A Christof Voemel %A Jack Dongarra %A Julien Langou %A Stanimire Tomov %K DOE_NANO %B J. Phys.: Conf. Ser. 46 %V :101088/1742-6596/46/1/040 %P 292-298 %8 2006-01 %G eng %0 Journal Article %J PARA 2006 %D 2006 %T Prospectus for the Next LAPACK and ScaLAPACK Libraries %A James Demmel %A Jack Dongarra %A B. Parlett %A William Kahan %A Ming Gu %A David Bindel %A Yozo Hida %A Xiaoye Li %A Osni Marques %A Jason E. Riedy %A Christof Voemel %A Julien Langou %A Piotr Luszczek %A Jakub Kurzak %A Alfredo Buttari %A Julien Langou %A Stanimire Tomov %B PARA 2006 %C Umea, Sweden %8 2006-06 %G eng %0 Conference Proceedings %B IEEE/ACM Proceedings of HPCNano SC06 (to appear) %D 2006 %T Towards bulk based preconditioning for quantum dot computations %A Andrew Canning %A Jack Dongarra %A Julien Langou %A Osni Marques %A Stanimire Tomov %A Christof Voemel %A Lin-Wang Wang %K doe-nano %B IEEE/ACM Proceedings of HPCNano SC06 (to appear) %8 2006-01 %G eng %0 Journal Article %J Journal of Computational Physics (submitted) %D 2006 %T The use of bulk states to accelerate the band edge state calculation of a semiconductor quantum dot %A Christof Voemel %A Stanimire Tomov %A Lin-Wang Wang %A Osni Marques %A Jack Dongarra %K doe-nano %B Journal of Computational Physics (submitted) %8 2006-01 %G eng