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Persistent URL http://purl.org/net/epubs/work/53474
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Record Id 53474
Title Generalized Golub-Kahan bidiagonalization and stopping criteria
Abstract The Golub-Kahan bidiagonalization algorithm has been widely used in solving least-squares problems and in the computation of the SVD of rectangular matrices. Here we propose an algo- rithm based on the Golub-Kahan process for the solution of augmented systems that minimizes the norm of the error and, in particular, we propose a novel estimator of the error similar to the one proposed by Hestenes-Stiefel for the conjugate gradient. This estimator gives a lower bound for the error, and can be used as a reliable stopping criterion for the whole process. We also pro- pose an upper bound of the error base on Gauss-Radau quadrature. Finally, we show how we can transform and optimally precondition augmented systems rising from the mixed finite-element approximation of differential problems.
Organisation CSE-NAG , STFC , SCI-COMP
Keywords Bidiagonalization , stopping criteria , Engineering
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Language English (EN)
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Journal Article SIAM J Matrix Anal A 34, no. 2 (2013): 86654, 593-623. doi:10.1137/120866543 86654.pdf 2013