Conjugate residual squared method and its improvement for non-symmetric linear systems

References

• Bücker , H. M. and Sauren , M. A parallel version of the quasi-minimal residual method based on coupled two-term recurrences . Proceedings of Workshop on Applied Parallel computing in Industrial Problems and Optimization (Para 96) . August , Lyngby, Denmark. Technical University of Denmark . Springer-Verlag
   Google Scholar
• Chi , L. H. , Liu , J. , Liu , X. P. , Hu , Q. F. and Li , X. M. An improved conjugate residual algorithm for large symmetric linear systems . Proceedings of the Joint Conference of ICCP6 and CCP2003 . Computational Physics , pp. 325 – 328 . New Jersey : Rinton Press .
   Google Scholar
• Freund , R. W. and Nachtigal , N. M. 1991 . QMR: a quasi-minimal residual method for non-Hermitian linear systems . Numer. Math. , 60 : 315 – 339 .
   Web of Science ®Google Scholar
• Gu , T. X. , Liu , X. P. and Mo , Z. Y. 2004 . Multiple search direction conjugate gradient method I: methods and their propositions . Int. J. Comput. Math. , 81 : 1133 – 1143 .
   Web of Science ®Google Scholar
• Gu , T. X. , Zuo , X. Y. , Zhang , L. T. , Zhang , W. Q. and Sheng , Z. Q. 2007 . An improved bi-conjugate residual algorithm suitable for distributed parallel computing . Appl. Math. Comput. , 186 : 1243 – 1253 .
   Web of Science ®Google Scholar
• Liu , X. P. , Gu , T. X. , Hang , X. D. and Sheng , Z. Q. 2006 . A parallel version of QMRCGSTAB method for large linear systems in distributed parallel environments . Appl. Math. Comput. , 172 : 744 – 752 .
   Google Scholar
• Saad , Y. 1996 . Iterative Methods for Sparse Linear Systems , Boston : PWS Publishing Company .
   Google Scholar
• Sogabe , T. and Zhang , S. L. 2003 . “ Extended conjugate residual methods for solving non-symmetric linear systems ” . In Numerical Linear Algebra and Optimization , Edited by: Ya-Xiang , Yuan . 88 – 99 . Beijing/New York : Science Press .
   Google Scholar
• Sonneveld , P. 1989 . CGS: a fast lanczos-type solver for nonsymmetric linear systems . SIAM J. Sci. Stat. Comput. , 10 : 36 – 52 .
   Web of Science ®Google Scholar
• de Sturler , E. 1996 . A performance model for Krylov subspace methods on mesh-based parallel computers . Parallel Comput. , 22 : 57 – 74 .
   Google Scholar
• de Sturler , E. and van der Vorst , H. A. 1995 . Reducing the effect of the global communication in GMRES(m) and CG on parallel distributed memory computers . Appl. Numer. Math. , 18 : 441 – 459 .
   Google Scholar
• van der Vorst , H. A. 1992 . Bi-CGSTAB: a fast and smoothly converging variant of bi-CG for the solution of nonsymmetric linear systems . SIAM J. Sci. Stat. Comput. , 13 : 631 – 644 .
   Web of Science ®Google Scholar
• Yang , T. R. The improved CGS method for large and sparse linear systems on bulk synchronous parallel architectures . 2002 5th International Conference on Algorithms and Architectures for Parallel Processing . pp. 232 – 237 . IEEE Computer Society .
   Google Scholar
• Yang , T. R. and Brent , R. P. The improved BiCGSTAB method for large and sparse nonsymmetric linear systems on parallel distributed memory architectures . 2001 5th International Conference on Algorithms and Architectures for Parallel Processing, IEEE Computer Society . pp. 324 – 328 .
   Google Scholar
• Yang , T. R. and Brent , R. P. 2003 . The improved BiCG method for large and sparse linear systems on parallel distributed memory architectures . Inf. J. , 6 : 349 – 360 .
   Google Scholar
• Yang , T. R. and Lin , H. X. The improved quasi-minimal residual method on massively distributed memory computers . Proceedings of The International Conference on High Performance Computing and Networking (HPCN-97) . April .
   Google Scholar