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Linear and Multilinear Algebra Volume 65, 2017 - Issue 3
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Articles

Improved convergence theorems for new Hermitian and skew-Hermitian splitting methods

Cui-Xia LiSchool of Mathematics and Statistics, Anyang Normal University, Anyang, P.R. China.Correspondence[email protected]
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Shi-Liang WuSchool of Mathematics and Statistics, Anyang Normal University, Anyang, P.R. China.View further author information
Pages 510-513 | Received 01 Jun 2015, Accepted 20 May 2016, Published online: 07 Jun 2016

References

  • Berman A, Plemmons RJ. Nonnegative matrices in the mathematical sciences. New York (NY): Academic Press; 1979. Reprinted by SIAM, Philadelphia (PA); 1994.
  • Varga RS. Matrix iterative analysis. Englewood Cliffs (NJ): Prentice-Hall; 1962.
  • Saad Y. Iterative methods for sparse linear systems. Boston (MA): PWS Publishing Company; 1996.
  • Bai Z-Z, Golub GH, Ng MK. Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems. SIAM J. Matrix Anal. Appl. 2003;24:603–626.
  • Bai Z-Z, Golub GH, Ng MK. On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations. Numer. Linear Algebra Appl. 2007;14:319–335.
  • Bai Z-Z, Ng MK. Erratum. Numer. Linear Algebra Appl. 2012;19:891.
  • Bai Z-Z, Golub GH, Lu L-Z, et al. Block triangular and skew-Hermitian splitting method for positive-definite linear systems. SIAM J. Sci. Comput. 2005;26:844–863.
  • Li C-X, Wu S-L. A modified GHSS method for non-Hermitian positive definite linear systems. Jpn. J. Ind. Appl. Math. 2012;29:253–268.
  • Benzi M. A generalization of the Hermitian and skew-Hermitian splitting iteration. SIAM J. Matrix Anal. Appl. 2009;31:360–374.
  • Bai Z-Z, Benzi M, Chen F. Modified HSS iteration methods for a class of complex symmetric linear systems. Computing. 2010;87:93–111.
  • Bai Z-Z, Golub GH, Pan J-Y. Perconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems. Numer. Math. 2004;98:1–32.
  • Bai Z-Z, Golub GH. Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems. IMA J. Numer. Anal. 2007;27:1–23.
  • Li X, Yang A-L, Wu Y-J. Lopsided PMHSS iteration method for a class of complex symmetric linear systems. Numer. Algor. 2014;66:555–568.
  • Li C-X, Wu S-L. A single-step HSS method for non-Hermitian positive definite linear systems. Appl. Math. Lett. 2015;44:26–29.
  • Wu S-L. Several variants of the Hermitian and skew-Hermitian splitting method for a class of complex symmetric linear systems. Numer. Linear Algebra Appl. 2015;22:338–356.
  • Bai Z-Z. Splitting iteration methods for non-Hermitian positive definite systems of linear equations. Hokkaido Math. J. 2007;36:801–814.
  • Pour HN, Goughery HS. New Hermitian and skew-Hermitian splitting methods for non-Hermitian positive-definite linear systems. Numer. Algor. 2015;69:207–225.

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