Bergische Universität Wuppertal
Fakultät für Mathematik und Naturwissenschaften
Angewandte Informatik - Algorithmik


Research project "Efficient parallel algorithms for singular value computations"

(Untersuchung, Entwicklung, Implementierung und vergleichende Bewertung paralleler Verfahren zur Singulärwertzerlegung)


Andreas Frommer
Benedikt Großer
Sabine Hofmann
Bruno Lang

Duration and funding

July 1994 to March 1999, funded by (Geschäftszeichen Fr 755/6-1 and Fr 755/6-2)


After a comparison of available methods for computing the SVD new approaches were developed and implemented:

Project-related publications

[1] Benedikt Großer and Bruno Lang. On symmetric eigenproblems induced by the bidiagonal SVD. SIAM J. Matrix Anal. Appl., 26(3):599--620, 2005. [ Abstract ]
[2] Benedikt Großer and Bruno Lang. An O( n2 ) algorithm for the bidiagonal SVD. Linear Algebra Appl., 358(1--3):45--70, January 2003. [ Abstract ]
[3] Christian H. Bischof, Bruno Lang, and Xiaobai Sun. A framework for symmetric band reduction. ACM Trans. Math. Software, 26(4):581--601, December 2000. [ Abstract ]
[4] Christian H. Bischof, Bruno Lang, and Xiaobai Sun. Algorithm 807: The SBR toolbox---software for successive band reduction. ACM Trans. Math. Software, 26(4):602--616, December 2000. [ Abstract ]
[5] Benedikt Großer and Bruno Lang. Efficient parallel reduction to bidiagonal form. Parallel Comput., 25(8):969--986, September 1999. [ Abstract ]
[6] Bruno Lang. Efficient eigenvalue and singular value computations on shared memory machines. Parallel Comput., 25(7):845--860, July 1999. [ Abstract ]
[7] Bruno Lang. Efficient algorithms for reducing banded matrices to bidiagonal and tridiagonal form. In Peter Arbenz, Marcin Paprzycki, Ahmed Sameh, and Vivek Sarin, editors, High Performance Algorithms for Structured Matrix Problems, volume 2 of Advances in the Theory of Computation and Computational Mathematics, pages 75--89. Nova Science Publishers, Commack, NY, 1998. [ Abstract ]

Project-related theses

[1] Benedikt Großer. Ein paralleler und hochgenauer O( n2 )-Algorithmus für die bidiagonale Singulärwertzerlegung. Dissertation, Bergische Universität Wuppertal, Germany, March 2001.
[2] Benedikt Großer. Parallele Reduktionsalgorithmen zur Berechnung der Singulärwertzerlegung. Diploma thesis, Bergische Universität Gesamthochschule Wuppertal, Germany, April 1997.

See also

the eigenvalue-related work on the Research page

University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics and Computer Science
Applied Computer Science Group

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