In this paper, we have presented a comparative study of the Lanczos solver with out preconditioning and conjugategradientsquared (CGS) solver with preconditioning for solving numerical heat transfer problem. Our com...
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In this paper, we have presented a comparative study of the Lanczos solver with out preconditioning and conjugategradientsquared (CGS) solver with preconditioning for solving numerical heat transfer problem. Our comparison is mainly focussed on the convergence and the CPU-time. (C) 1999 Elsevier Science Ltd. Ail rights reserved.
Recently Van der Vorst [SLAM J. Sci. Statist. Comput., 13 (1992), pp. 631-644] proposed for solving nonsymmetric linear systems Az = b a biconjugategradient (BICG)-based Krylov space method called BICGSTAB that, like...
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Recently Van der Vorst [SLAM J. Sci. Statist. Comput., 13 (1992), pp. 631-644] proposed for solving nonsymmetric linear systems Az = b a biconjugategradient (BICG)-based Krylov space method called BICGSTAB that, like the biconjugategradientsquared (BICGS) method of Sonneveld, does not require matrix-vector multiplications with the transposed matrix A(T), and that has typically a much smoother convergence behavior than BICG and BICGS. Its nth residual polynomial is the product of the one of BICG (i.e., the nth Lanczos polynomial) with a polynomial of the same degree with real zeros. Therefore, nonreal eigenvalues of A are not approximated well by the second polynomial factor. Here, the author presents for real nonsymmetric matrices a method BICGSTAB2 in which the second factor may have complex conjugate zeros. Moreover, versions suitable for complex matrices are given for both methods.
The conjugate gradient squared algorithm can suffer of similar breakdowns as Lanczos type methods for the same reason that is the non-existence of some formal orthogonal polynomials. Thus curing such breakdowns is pos...
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