Lanczos-type variants of the COCR method for complex nonsymmetric linear systems

  • Authors:

  • Yan-Fei Jing;Ting-Zhu Huang;Yong Zhang;Liang Li;Guang-Hui Cheng;Zhi-Gang Ren;Yong Duan;Tomohiro Sogabe;Bruno Carpentieri

  • Affiliations:

  • School of Applied Mathematics/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China;School of Applied Mathematics/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China;School of Applied Mathematics/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China;School of Applied Mathematics/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China;School of Applied Mathematics/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China;School of Applied Mathematics/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China;School of Applied Mathematics/Institute of Computational Science, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, PR China;Department of Computational Science and Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan;CRS4 Bioinformatics Laboratory, Edificio 3, Loc. Piscinamanna, 09010 Pula (CA), Italy

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2009

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Abstract

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 Pocock and Walker [M.D. Pocock, S.P. Walker, The complex Bi-conjugate Gradient solver applied to large electromagnetic scattering problems, computational costs, and cost scalings, IEEE Trans. Antennas Propagat. 45 (1997) 140-146], three Lanczos-type variants of the recent Conjugate A-Orthogonal Conjugate Residual (COCR) method of Sogabe and Zhang [T. Sogabe, S.-L. Zhang, A COCR method for solving complex symmetric linear systems, J. Comput. Appl. Math. 199 (2007) 297-303] 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 Sogabe's Ph.D. Dissertation. 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 University of Florida Sparse Matrix Collection by Davis.