Abstract
In this paper, we propose new product-type iterative methods by introducing the BiCGSafe strategy, i.e., utilization of associate residual in place of residual, to the variants of GPBiCG. We refer to BiCGStar (BiCG with stabilization of associate residual) and its improved version of BiCGStar method. BiCGStar and BiCGStar-plus methods outperform compared with the conventional iterative methods. Moreover, our proposed methods are suited to parallel computer with distributed memory systems, since they require single global synchronization per one iteration.
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References
Abe, K., Sleijpen, G.L.G.: Solving linear equations with a stabilized GPBiCG mehtod. Appl. Numer. Math. 67, 4–16 (2013)
Abe, K., Sleijpen, G.L.G.: Hybrid Bi-CG methods with Bi-CG formulation closer to the IDR approach. Appl. Math. Comput. 218, 10889–10899 (2012)
Florida Sparse Matrix Collection, http://www.cise.ufl.edu/research/sparse/matrices/index.html
Fujino, S., Fujiwara, M., Yoshida, M.: A proposal of preconditioned BiCGSafe method with safe convergence. In: Proc. of the 17th IMACS World Congress on Scientific Computation, Appl. Math. Simul. CD-ROM, Paris (2005)
Rutishauser, H.: Theory of gradient method, Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self-Adjoint Boundary Value Problems. Mitt. Inst. Angew. Math, pp. 24–49. ETH Zürich, Birkhäuser (1959)
Sleijpen, G.L.G., Sonneveld, P., van Gijzen, M.B.: Bi-CGSTAB as an induced dimension reduction method. Appl. Numer. Math. 60, 1100–1114 (2010)
Sonneveld, P., van Gijzen, M.B.: IDR(s): a family of simple and fast algorithms for solving large nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 31(2), 1035–1062 (2008)
Zhang, S.-L.: GPBi-CG: Generalized product-type methods based on Bi-CG for solving nonsymmetric linear systems. SIAM J. Sci. Comput. 18, 537–551 (1997)
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Fujino, S., Murakami, K. (2013). A Parallel Variant of BiCGStar-Plus Method Reduced to Single Global Synchronization. In: Tan, G., Yeo, G.K., Turner, S.J., Teo, Y.M. (eds) AsiaSim 2013. AsiaSim 2013. Communications in Computer and Information Science, vol 402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45037-2_30
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DOI: https://doi.org/10.1007/978-3-642-45037-2_30
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