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LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation Between Regular Matrix Pairs
Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, HPC2N (High Performance Computing Centre North).
Umeå University, Faculty of Science and Technology, Department of Computing Science. Umeå University, Faculty of Science and Technology, HPC2N (High Performance Computing Centre North).
1996 (English)In: ACM Transactions on Mathematical Software, Vol. 22, no 1, 78-103 p.Article in journal (Refereed) Published
Abstract [en]

Robust and fast software to solve the generalized Sylvester equation (AR - LB = C, DR - LE = F) for unknowns R and L is presented. This special linear system of equations, and its transpose, arises in computing error bounds for computed eigenvalues and eigenspaces of the generalized eigenvalue problem S - lambda T, in computing deflating subspaces of the same problem, and in computing certain decompositions of transfer matrices arising in control theory. Our contributions are twofold. First, we reorganize the standard algorithm for this problem to use Level 3 BLAS operations, like matrix multiplication, in its inner loop. This speeds up the algorithm by a factor of 9 on an IBM RS6000. Second, we develop and compare several condition estimation algorithms, which inexpensively but accurately estimate the sensitivity of the solution of this linear system.

Place, publisher, year, edition, pages
1996. Vol. 22, no 1, 78-103 p.
Identifiers
URN: urn:nbn:se:umu:diva-21957ISBN: 0098-3500 OAI: oai:DiVA.org:umu-21957DiVA: diva2:212216
Available from: 2009-04-21 Created: 2009-04-21 Last updated: 2009-07-09

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<Go to ISI>://A1996UD40300007

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Kågström, Bo

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