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On product-type generalized block AOR method for augmented linear systems
A generalization of the positive-definite and skew-Hermitian splitting iteration
1. | School of Transportation, Nantong University, Nantong, 226019, China |
2. | School of Mathematical Sciences, Soochow University, Suzhou, 215006, China, China |
References:
[1] |
Z.-Z. Bai, Optimal parameters in the HSS-like methods for saddle point problems, Numer. Linear Algebra Appl., 16 (2009), 447-479.
doi: 10.1002/nla.626. |
[2] |
Z.-Z. Bai, On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems, Computing, 89 (2010), 171-197.
doi: 10.1007/s00607-010-0101-. |
[3] |
Z.-Z. Bai, M. Benzi and F. Chen, Modified HSS iteration methods for a class of complex symmetric linear systems, Computing, 87 (2010), 93-111.
doi: 10.1007/s00607-010-0077-0. |
[4] |
Z.-Z. Bai, M. Benzi and F. Chen, On preconditioned MHSS iteration methods for complex symmetric linear systems, Numer. Algor., 56 (2011), 297-317.
doi: 10.1007/s11075-010-9441-6. |
[5] |
Z.-Z. Bai and G. H. Golub, Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems, IMA J. Numer. Anal., 27 (2007), 1-23.
doi: 10.1093/imanum/drl017. |
[6] |
Z.-Z. Bai, G. H. Golub and C.-K. Li, Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices, SIAM J. Sci. Comput., 28 (2006), 583-603.
doi: 10.1137/050623644. |
[7] |
Z.-Z. Bai, G. H. Golub, L.-Z. Lu and J.-F. Yin, Block triangular and skew-Hermitian splitting methods for positive-definite linear systems, SIAM J. Sci. Comput., 23 (2005), 844-863.
doi: 10.1137/S1064827503428114. |
[8] |
Z.-Z. Bai, G. H. Golub and M. K. Ng, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl., 24 (2003), 603-626.
doi: 10.1137/S0895479801395458. |
[9] |
Z.-Z. Bai, G. H. Golub and M. K. Ng, On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations, Numer. Linear Algebra Appl., 14 (2007), 319-335.
doi: 10.1002/nla.517. |
[10] |
Z.-Z. Bai, G. H. Golub and M. K. Ng, On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, Linear Algebra Appl., 428 (2008), 413-440.
doi: 10.1016/j.laa.2007.02.018. |
[11] |
Z.-Z. Bai, G. H. Golub and J.-Y. Pan, Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems, Numer. Math., 98 (2004), 1-32. |
[12] |
M. Benzi, A generalization of the Hermitian and skew-Hermitian splitting iteration, SIAM J. Matrix Anal. Appl., 31 (2009), 360-374.
doi: 10.1137/080723181. |
[13] |
M. Benzi, M. J. Gander and G. H Golub, Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems, BIT, 43 (2003), 881-900.
doi: 10.1023/B:BITN.0000014548.26616.65. |
[14] |
M. Benzi and G. H. Golub, A preconditioner for generalized saddle point problems, SIAM J. Matrix Anal. Appl., 26 (2004), 20-41.
doi: 10.1137/S0895479802417106. |
[15] |
M. Benzi and X.-P. Guo, A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations, Appl. Numer. Math., 61 (2011), 66-76.
doi: 10.1016/j.apnum.2010.08.005. |
[16] |
L. C. Chan, M. K. Ng and N. K. Tsing, Spectral Analysis for HSS Preconditioners, Numer. Math. Theor. Meth. Appl., 1 (2008), 57-77. |
[17] |
M.-Q. Jiang and Y. Cao, On local Hermitian and skew-Hermitian splitting iteration methods for generalized saddle point problems, J. Comput. Appl. Math., 231 (2009), 973-982.
doi: 10.1016/j.cam.2009.05.012. |
[18] |
L. Li, T.-Z. Huang and X.-P. Liu, Asymmetric Hermitian and skew-Hermitian splitting methods for positive definite linear systems, Comput. Math. Appl., 54 (2007), 147-159.
doi: 10.1016/j.camwa.2006.12.024. |
[19] |
J.-Y. Pan, M. K. Ng and Z.-Z. Bai, New preconditioners for saddle point problems, Appl. Math. Comput., 172 (2006), 762-771.
doi: 10.1016/j.amc.2004.11.016. |
[20] |
D. W. Peaceman and H. H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl.Math., 3 (1955), 28-41.
doi: 10.1137/0103003. |
[21] |
Y. Saad, "Iterative Methods for Sparse Linear Systems," 2nd edition, SIAM, Philadelphia, 2003.
doi: 10.1137/1.9780898718003. |
[22] |
A.-L Yang, J. An and Y.-J. Wu, A generalized preconditioned HSS method for non-Hermitian positive definite linear systems, Appl. Math. Comput., 216 (2010), 1715-1722.
doi: 10.1016/j.amc.2009.12.032. |
show all references
References:
[1] |
Z.-Z. Bai, Optimal parameters in the HSS-like methods for saddle point problems, Numer. Linear Algebra Appl., 16 (2009), 447-479.
doi: 10.1002/nla.626. |
[2] |
Z.-Z. Bai, On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems, Computing, 89 (2010), 171-197.
doi: 10.1007/s00607-010-0101-. |
[3] |
Z.-Z. Bai, M. Benzi and F. Chen, Modified HSS iteration methods for a class of complex symmetric linear systems, Computing, 87 (2010), 93-111.
doi: 10.1007/s00607-010-0077-0. |
[4] |
Z.-Z. Bai, M. Benzi and F. Chen, On preconditioned MHSS iteration methods for complex symmetric linear systems, Numer. Algor., 56 (2011), 297-317.
doi: 10.1007/s11075-010-9441-6. |
[5] |
Z.-Z. Bai and G. H. Golub, Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems, IMA J. Numer. Anal., 27 (2007), 1-23.
doi: 10.1093/imanum/drl017. |
[6] |
Z.-Z. Bai, G. H. Golub and C.-K. Li, Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices, SIAM J. Sci. Comput., 28 (2006), 583-603.
doi: 10.1137/050623644. |
[7] |
Z.-Z. Bai, G. H. Golub, L.-Z. Lu and J.-F. Yin, Block triangular and skew-Hermitian splitting methods for positive-definite linear systems, SIAM J. Sci. Comput., 23 (2005), 844-863.
doi: 10.1137/S1064827503428114. |
[8] |
Z.-Z. Bai, G. H. Golub and M. K. Ng, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl., 24 (2003), 603-626.
doi: 10.1137/S0895479801395458. |
[9] |
Z.-Z. Bai, G. H. Golub and M. K. Ng, On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations, Numer. Linear Algebra Appl., 14 (2007), 319-335.
doi: 10.1002/nla.517. |
[10] |
Z.-Z. Bai, G. H. Golub and M. K. Ng, On inexact Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, Linear Algebra Appl., 428 (2008), 413-440.
doi: 10.1016/j.laa.2007.02.018. |
[11] |
Z.-Z. Bai, G. H. Golub and J.-Y. Pan, Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems, Numer. Math., 98 (2004), 1-32. |
[12] |
M. Benzi, A generalization of the Hermitian and skew-Hermitian splitting iteration, SIAM J. Matrix Anal. Appl., 31 (2009), 360-374.
doi: 10.1137/080723181. |
[13] |
M. Benzi, M. J. Gander and G. H Golub, Optimization of the Hermitian and skew-Hermitian splitting iteration for saddle-point problems, BIT, 43 (2003), 881-900.
doi: 10.1023/B:BITN.0000014548.26616.65. |
[14] |
M. Benzi and G. H. Golub, A preconditioner for generalized saddle point problems, SIAM J. Matrix Anal. Appl., 26 (2004), 20-41.
doi: 10.1137/S0895479802417106. |
[15] |
M. Benzi and X.-P. Guo, A dimensional split preconditioner for Stokes and linearized Navier-Stokes equations, Appl. Numer. Math., 61 (2011), 66-76.
doi: 10.1016/j.apnum.2010.08.005. |
[16] |
L. C. Chan, M. K. Ng and N. K. Tsing, Spectral Analysis for HSS Preconditioners, Numer. Math. Theor. Meth. Appl., 1 (2008), 57-77. |
[17] |
M.-Q. Jiang and Y. Cao, On local Hermitian and skew-Hermitian splitting iteration methods for generalized saddle point problems, J. Comput. Appl. Math., 231 (2009), 973-982.
doi: 10.1016/j.cam.2009.05.012. |
[18] |
L. Li, T.-Z. Huang and X.-P. Liu, Asymmetric Hermitian and skew-Hermitian splitting methods for positive definite linear systems, Comput. Math. Appl., 54 (2007), 147-159.
doi: 10.1016/j.camwa.2006.12.024. |
[19] |
J.-Y. Pan, M. K. Ng and Z.-Z. Bai, New preconditioners for saddle point problems, Appl. Math. Comput., 172 (2006), 762-771.
doi: 10.1016/j.amc.2004.11.016. |
[20] |
D. W. Peaceman and H. H. Rachford Jr., The numerical solution of parabolic and elliptic differential equations, J. Soc. Indust. Appl.Math., 3 (1955), 28-41.
doi: 10.1137/0103003. |
[21] |
Y. Saad, "Iterative Methods for Sparse Linear Systems," 2nd edition, SIAM, Philadelphia, 2003.
doi: 10.1137/1.9780898718003. |
[22] |
A.-L Yang, J. An and Y.-J. Wu, A generalized preconditioned HSS method for non-Hermitian positive definite linear systems, Appl. Math. Comput., 216 (2010), 1715-1722.
doi: 10.1016/j.amc.2009.12.032. |
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