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Title: New implementation of QMR-type algorithms
Authors: García, M. D.
Florez, E. 
Suárez Sarmiento, Antonio F. 
González, L. 
Montero, G. 
UNESCO Clasification: 12 Matemáticas
1206 Análisis numérico
Keywords: Krylov subspace methods
Nonsymmetric linear systems
Quasi-minimal residual methods
Sparse matrices
Issue Date: 2005
Project: Simulacion Numerica de Campos de Viento Orientados A Procesos Atmofericos. 
Journal: Computers and Structures 
Conference: 9th International Conference on Civil and Structural Engineering Computing/7th International Conference on the Application of Artificial Intelligence to Civil and Structural Engineering 
Abstract: Quasi-minimal residual algorithms, these are QMR, TFQMR and QMRCGSTAB, are biorthogonalisation methods for solving nonsymmetric linear systems of equations which improve the irregular behaviour of BiCG, CGS and BiCGSTAB algorithms, respectively. They are based on the quasi-minimisation of the residual using the standard Givens rotations that lead to iterations with short term recurrences. In this paper, these quasi-minimisation problems are solved using a different direct solver which provides new versions of QMR-type methods, the modified QMR methods (MQMR). MQMR algorithms have different convergence behaviour in finite arithmetic although are equivalent to the standard ones in exact arithmetic. The new implementations may reduce the number of iterations in some cases. In addition, we study the effect of reordering and preconditioning with Jacobi, ILU, SSOR or sparse approximate inverse preconditioners on the performance of these algorithms. Some numerical experiments are solved in order to compare the results obtained by standard and modified algorithms.
ISSN: 0045-7949
DOI: 10.1016/j.compstruc.2005.03.026
Source: Computers and Structures [ISSN 0045-7949], v. 83 (28-30), p. 2414-2422
Appears in Collections:Actas de congresos
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