Research project "Efficient parallel algorithms for singular value computations"

Andreas Frommer
Benedikt Großer
Sabine Hofmann
Bruno Lang

July 1994 to March 1999, funded by Deutsche Forschungsgemeinschaft (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:

a two-step algorithm for reduction to bidiagonal form
a "coupling" approach that allows using the highly efficient MRRR algorithm for the bidiagonal SVD

[1]	Benedikt Großer and Bruno Lang. On symmetric eigenproblems induced by the bidiagonal SVD. SIAM J. Matrix Anal. Appl., 26(3):599--620, 2005. [ DOI \| 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. [ DOI \| 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. [ DOI \| 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. [ DOI \| Abstract ]
[5]	Benedikt Großer and Bruno Lang. Efficient parallel reduction to bidiagonal form. Parallel Comput., 25(8):969--986, September 1999. [ DOI \| Abstract ]
[6]	Bruno Lang. Efficient eigenvalue and singular value computations on shared memory machines. Parallel Comput., 25(7):845--860, July 1999. [ DOI \| 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 ]