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Fast secant methods for the iterative solution of large nonsymmetric linear systemsA family of secant methods based on general rank-1 updates was revisited in view of the construction of iterative solvers for large non-Hermitian linear systems. As it turns out, both Broyden's good and bad update techniques play a special role, but should be associated with two different line search principles. For Broyden's bad update technique, a minimum residual principle is natural, thus making it theoretically comparable with a series of well known algorithms like GMRES. Broyden's good update technique, however, is shown to be naturally linked with a minimum next correction principle, which asymptotically mimics a minimum error principle. The two minimization principles differ significantly for sufficiently large system dimension. Numerical experiments on discretized partial differential equations of convection diffusion type in 2-D with integral layers give a first impression of the possible power of the derived good Broyden variant.
Document ID
19920002437
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Deuflhard, Peter (Research Inst. for Advanced Computer Science Moffett Field, CA, United States)
Freund, Roland (Research Inst. for Advanced Computer Science Moffett Field, CA, United States)
Walter, Artur (Research Inst. for Advanced Computer Science Moffett Field, CA, United States)
Date Acquired
September 6, 2013
Publication Date
July 1, 1990
Subject Category
Computer Programming And Software
Report/Patent Number
NAS 1.26:188867
RIACS-TR-90-31
NASA-CR-188867
Accession Number
92N11655
Funding Number(s)
CONTRACT_GRANT: NCC2-387
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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