@techreport {1194, title = {Bidiagonal SVD Computation via an Associated Tridiagonal Eigenproblem}, journal = {LAPACK Working Note}, number = {LAWN 295, ICL-UT-18-02}, year = {2018}, month = {2018-04}, publisher = {University of Tennessee}, abstract = {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.}, author = {Osni Marques and James Demmel and Paulo B. Vasconcelos} } @inproceedings {icl:416, title = {Interior State Computation of Nano Structures}, journal = {PARA 2008, 9th International Workshop on State-of-the-Art in Scientific and Parallel Computing}, year = {2008}, month = {2008-05}, address = {Trondheim, Norway}, author = {Andrew Canning and Jack Dongarra and Julien Langou and Osni Marques and Stanimire Tomov and Christof Voemel and Lin-Wang Wang} } @article {icl:447, title = {State-of-the-Art Eigensolvers for Electronic Structure Calculations of Large Scale Nano-Systems}, journal = {Journal of Computational Physics}, volume = {227}, number = {15}, year = {2008}, month = {2008-01}, pages = {7113-7124}, author = {Christof Voemel and Stanimire Tomov and Osni Marques and Andrew Canning and Lin-Wang Wang and Jack Dongarra} } @article {icl:401, title = {The Use of Bulk States to Accelerate the Band Edge State Calculation of a Semiconductor Quantum Dot}, journal = {Journal of Computational Physics}, volume = {223}, year = {2007}, month = {2007-00}, pages = {774-782}, author = {Christof Voemel and Stanimire Tomov and Lin-Wang Wang and Osni Marques and Jack Dongarra} } @inproceedings {icl:325, title = {Performance evaluation of eigensolvers in nano-structure computations}, journal = {IEEE/ACM Proceedings of HPCNano SC06 (to appear)}, year = {2006}, month = {2006-01}, keywords = {doe-nano}, author = {Andrew Canning and Jack Dongarra and Julien Langou and Osni Marques and Stanimire Tomov and Christof Voemel and Lin-Wang Wang} } @article {icl:327, title = {Predicting the electronic properties of 3D, million-atom semiconductor nanostructure architectures}, journal = {J. Phys.: Conf. Ser. 46}, volume = {:101088/1742-6596/46/1/040}, year = {2006}, month = {2006-01}, pages = {292-298}, keywords = {DOE_NANO}, author = {Alex Zunger and Alberto Franceschetti and Gabriel Bester and Wesley B. Jones and Kwiseon Kim and Peter A. Graf and Lin-Wang Wang and Andrew Canning and Osni Marques and Christof Voemel and Jack Dongarra and Julien Langou and Stanimire Tomov} } @article {icl:370, title = {Prospectus for the Next LAPACK and ScaLAPACK Libraries}, journal = {PARA 2006}, year = {2006}, month = {2006-06}, address = {Umea, Sweden}, author = {James Demmel and Jack Dongarra and B. Parlett and William Kahan and Ming Gu and David Bindel and Yozo Hida and Xiaoye Li and Osni Marques and Jason E. Riedy and Christof Voemel and Julien Langou and Piotr Luszczek and Jakub Kurzak and Alfredo Buttari and Julien Langou and Stanimire Tomov} } @inproceedings {icl:324, title = {Towards bulk based preconditioning for quantum dot computations}, journal = {IEEE/ACM Proceedings of HPCNano SC06 (to appear)}, year = {2006}, month = {2006-01}, keywords = {doe-nano}, author = {Andrew Canning and Jack Dongarra and Julien Langou and Osni Marques and Stanimire Tomov and Christof Voemel and Lin-Wang Wang} } @article {icl:326, title = {The use of bulk states to accelerate the band edge state calculation of a semiconductor quantum dot}, journal = {Journal of Computational Physics (submitted)}, year = {2006}, month = {2006-01}, keywords = {doe-nano}, author = {Christof Voemel and Stanimire Tomov and Lin-Wang Wang and Osni Marques and Jack Dongarra} }