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Flexible GPBi-CG Method for Nonsymmetric Linear Systems

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DOI: 10.4236/am.2012.34050    4,779 Downloads   7,775 Views   Citations

ABSTRACT

We present a flexible version of GPBi-CG algorithm which allows for the use of a different preconditioner at each step of the algorithm. In particular, a result of the flexibility of the variable preconditioner is to use any iterative method. For example, the standard GPBi-CG algorithm itself can be used as a preconditioner, as can other Krylov subspace methods or splitting methods. Numerical experiments are conducted for flexible GPBi-CG for a few matrices including some nonsymmetric matrices. These experiments illustrate the convergence and robustness of the flexible iterative method.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

J. Wang and T. Gu, "Flexible GPBi-CG Method for Nonsymmetric Linear Systems," Applied Mathematics, Vol. 3 No. 4, 2012, pp. 331-335. doi: 10.4236/am.2012.34050.

References

[1] Y. Notay, “Flexible Conjugate Gradients,” SIAM Journal on Scientific Computing, Vol. 22, No. 4, 2000, pp. 14441460. doi:10.1137/S1064827599362314
[2] Y. Saad, “A Flexible Inner-Outer Preconditioned GMRES Algorithm,” SIAM Journal on Scientific Computing, Vol. 14, No. 2, 1993, pp. 461-469. doi:10.1137/0914028
[3] D. B. Szyld and J. A. Vogel, “FQMR: A Flexible QuasiMinimal Residual Method with Inexact Preconditioning,” SIAM Journal on Scientific Computing, Vol. 23, No. 2, 2001, pp. 363-380. doi:10.1137/S106482750037336X
[4] K. Abe and S.-L. Zhang, “A Variable Preconditioning Using The SOR Method For GCR-like Methods,” International Journal of Numerical Analysis and Modeling, Vol. 2, No.2, 2005, pp. 147-161.
[5] J. A. Vogel, “Flexible BiCG and Flexible Bi-CGSTAB for Nonsymmetric Linear Systems,” Applied Mathematics and Computation, Vol. 188, No. 1, 2007, pp. 226-233. doi:10.1016/j.amc.2006.09.116
[6] S.-L. Zhang, “GPBi-CG: Generalized Product-Type Methods Baseed on Bi-CG for Solving Nonsymentric Linear Systems,” SIAM Journal on Scientific Computing, Vol. 18, No. 2, 1997, pp. 537-551. doi:10.1137/S1064827592236313
[7] Y. Saad, “Iterative Method for Solving Linear Systems,” 2nd Edition, SIAM, Philadelphia, 2003. doi:10.1137/1.9780898718003

  
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