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Lanczos-type variants of the COCR method for complex nonsymmetric linear systems. (English) Zbl 1173.65316
Summary: Motivated by the celebrated extending applications of the well-established Complex Biconjugate Gradient (CBiCG) method to deal with large three-dimensional electromagnetic scattering problems by M. D. Pocock and S. P. Walker [IEEE Trans. Antennas Propagat. 45, No. 1, 140–146 (1997)], three Lanczos-type variants of the recently introduced Conjugate $A$-Orthogonal Conjugate Residual (COCR) method by T. Sogabe and S.-L. Zhang [J. Comput. Appl. Math. 199, No. 2, 297–303 (2007; Zbl 1108.65028)] are explored for the solution of complex nonsymmetric linear systems. The first two can be respectively considered as mathematically equivalent but numerically improved popularizing versions of the BiCR and CRS methods for complex systems presented in T. Sogabe’s Ph.D. Dissertation [Extensions of the conjugate residual method, University of Tokyo (2006)]. And the last one is somewhat new and is a stabilized and more smoothly converging variant of the first two in some circumstances. The presented algorithms are with the hope of obtaining smoother and, hopefully, faster convergence behavior in comparison with the CBiCG method as well as its two corresponding variants. This motivation is demonstrated by numerical experiments performed on some selective matrices borrowed from the sparse matrix collection of the University of Florida by Davis.
##### MSC:
 65F10 Iterative methods for linear systems
##### Software:
SparseMatrix; CGS