The BL-QMR algorithm for non-Hermitian linear systems with multiple right-hand sides [electronic resource]
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| Online Access: |
Online Access (via OSTI) |
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| Format: | Government Document Electronic eBook |
| Language: | English |
| Published: |
Oak Ridge, Tenn. :
distributed by the Office of Scientific and Technical Information, U.S. Department of Energy,
1996.
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| Subjects: |
| Abstract: | Many applications require the solution of multiple linear systems that have the same coefficient matrix, but differ in their right-hand sides. Instead of applying an iterative method to each of these systems individually, it is potentially much more efficient to employ a block version of the method that generates iterates for all the systems simultaneously. However, it is quite intricate to develop robust and efficient block iterative methods. In particular, a key issue in the design of block iterative methods is the need for deflation. The iterates for the different systems that are produced by a block method will, in general, converge at different stages of the block iteration. An efficient and robust block method needs to be able to detect and then deflate converged systems. Each such deflation reduces the block size, and thus the block method needs to be able to handle varying block sizes. For block Krylov-subspace methods, deflation is also crucial in order to delete linearly and almost linearly dependent vectors in the underlying block Krylov sequences. An added difficulty arises for Lanczos-type block methods for non-Hermitian systems, since they involve two different block Krylov sequences. In these methods, deflation can now occur independently in both sequences, and consequently, the block sizes in the two sequences may become different in the course of the iteration, even though they were identical at the beginning. We present a block version of Freund and Nachtigal̀s quasi-minimal residual method for the solution of non-Hermitian linear systems with single right-hand sides. |
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| Item Description: | Published through SciTech Connect. 12/31/1996. "conf-9604167--vol.2" "DE96015307" Copper Mountain conference on iterative methods, Copper Mountain, CO (United States), 9-13 Apr 1996. Freund, R.W. [AT&T Bell Labs., Murray Hill, NJ (United States)] Front Range Scientific Computations, Inc., Lakewood, CO (United States) |
| Physical Description: | pp. 1, Paper 40 : digital, PDF file. |