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A new Bramble-Pasciak-like preconditioner for saddle point problems
Newton-MHSS methods for solving systems of nonlinear equations with complex symmetric Jacobian matrices
1. | School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China, China |
References:
[1] |
H. B. An and Z. Z. Bai, A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations, Appl. Numer. Math., 57 (2007), 235-252.
doi: 10.1016/j.apnum.2006.02.007. |
[2] |
I. S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equation, Rev. Mod. Phys., 74 (2002), 99-143.
doi: 10.1103/RevModPhys.74.99. |
[3] |
Z. Z. Bai, On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems, Computing, 89 (2010), 171-197. |
[4] |
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. |
[5] |
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. |
[6] |
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 (2002), 603-626.
doi: 10.1137/S0895479801395458. |
[7] |
Z.-Z. Bai and X.-P. Guo, On Newton-HSS methods for systems of nonlinear equations with positive-definite jacobian matrices, J. Comput. Math., 28 (2010), 235-260. |
[8] |
Z. Z. Bai and X. Yang, On HSS-based iteration methods for weakly nonlinear systems, Appl. Numer. Math., 59 (2009), 2923-2936.
doi: 10.1016/j.apnum.2009.06.005. |
[9] |
M. Benzi and D. B. Szyld, Existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods, Numer. Math., 76 (1997), 309-321.
doi: 10.1007/s002110050265. |
[10] |
T. Bohr, M. H. Jensen, G. Paladin and A. Vulpiani, "Dynamical Systems Approach to Turbulence," Cambridge University Press, 1998.
doi: 10.1017/CBO9780511599972. |
[11] |
R. Dembo, S. Eisenstat and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal., 19 (1982), 400-408.
doi: 10.1137/0719025. |
[12] |
P. Deuflhard, "Newton Methods for Nonlinear Problems," Springer-Verlag, Berlin Heidelberg, 2004. |
[13] |
S. C. Eisenstat and H. F. Walker, Globally convergent inexact Newton methods, SIAM J. Optim., 4 (1994), 393-422.
doi: 10.1137/0804022. |
[14] |
S. C. Eisenstat and H. F. Walker, Choosing the forcing terms in an inexact Newton method, SIAM J. Sci. Comput., 17 (1996), 16-32.
doi: 10.1137/0917003. |
[15] |
X. P. Guo and I. S. Duff, Semilocal and global convergence of the Newton-HSS method for systems of nonlinear equations, Numer. Linear Algebra Appl., 18 (2011), 299-315.
doi: 10.1002/nla.713. |
[16] |
C. T. Kelley, "Iterative Methods for Linear and Nonlinear Equations," SIAM, Philadelphia, PA, 1995.
doi: 10.1137/1.9781611970944. |
[17] |
Y. Kuramoto, "Chemical Oscillations, Waves, and Turbulence," Dover Publications, Inc., Mineola, New York, 2003. |
[18] |
J. M. Ortega and W. C. Rheinboldt, "Iterative Solution of Nonlinear Equations in Several Variables," SIAM, Philadelphia, PA, 2000.
doi: 10.1137/1.9780898719468. |
[19] |
M. Pernice and H. F. Walker, Nitsol: A newton iterative solver for nonlinear systems, SIAM J. Sci. Comput., 19 (1998), 302-318.
doi: 10.1137/S1064827596303843. |
[20] |
Y. Saad, "Iterative Methods for Sparse Linear Systems," 2nd edition, SIAM, Philadelphia, PA, 2003.
doi: 10.1137/1.9780898718003. |
[21] |
C. Sulem and P. L. Sulem, "The Nonlinear Schrödinger Equation, Self-focusing and Wave Collapse," Springer Verlag, New York, 1999. |
[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] |
H. B. An and Z. Z. Bai, A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations, Appl. Numer. Math., 57 (2007), 235-252.
doi: 10.1016/j.apnum.2006.02.007. |
[2] |
I. S. Aranson and L. Kramer, The world of the complex Ginzburg-Landau equation, Rev. Mod. Phys., 74 (2002), 99-143.
doi: 10.1103/RevModPhys.74.99. |
[3] |
Z. Z. Bai, On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems, Computing, 89 (2010), 171-197. |
[4] |
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. |
[5] |
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. |
[6] |
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 (2002), 603-626.
doi: 10.1137/S0895479801395458. |
[7] |
Z.-Z. Bai and X.-P. Guo, On Newton-HSS methods for systems of nonlinear equations with positive-definite jacobian matrices, J. Comput. Math., 28 (2010), 235-260. |
[8] |
Z. Z. Bai and X. Yang, On HSS-based iteration methods for weakly nonlinear systems, Appl. Numer. Math., 59 (2009), 2923-2936.
doi: 10.1016/j.apnum.2009.06.005. |
[9] |
M. Benzi and D. B. Szyld, Existence and uniqueness of splittings for stationary iterative methods with applications to alternating methods, Numer. Math., 76 (1997), 309-321.
doi: 10.1007/s002110050265. |
[10] |
T. Bohr, M. H. Jensen, G. Paladin and A. Vulpiani, "Dynamical Systems Approach to Turbulence," Cambridge University Press, 1998.
doi: 10.1017/CBO9780511599972. |
[11] |
R. Dembo, S. Eisenstat and T. Steihaug, Inexact Newton methods, SIAM J. Numer. Anal., 19 (1982), 400-408.
doi: 10.1137/0719025. |
[12] |
P. Deuflhard, "Newton Methods for Nonlinear Problems," Springer-Verlag, Berlin Heidelberg, 2004. |
[13] |
S. C. Eisenstat and H. F. Walker, Globally convergent inexact Newton methods, SIAM J. Optim., 4 (1994), 393-422.
doi: 10.1137/0804022. |
[14] |
S. C. Eisenstat and H. F. Walker, Choosing the forcing terms in an inexact Newton method, SIAM J. Sci. Comput., 17 (1996), 16-32.
doi: 10.1137/0917003. |
[15] |
X. P. Guo and I. S. Duff, Semilocal and global convergence of the Newton-HSS method for systems of nonlinear equations, Numer. Linear Algebra Appl., 18 (2011), 299-315.
doi: 10.1002/nla.713. |
[16] |
C. T. Kelley, "Iterative Methods for Linear and Nonlinear Equations," SIAM, Philadelphia, PA, 1995.
doi: 10.1137/1.9781611970944. |
[17] |
Y. Kuramoto, "Chemical Oscillations, Waves, and Turbulence," Dover Publications, Inc., Mineola, New York, 2003. |
[18] |
J. M. Ortega and W. C. Rheinboldt, "Iterative Solution of Nonlinear Equations in Several Variables," SIAM, Philadelphia, PA, 2000.
doi: 10.1137/1.9780898719468. |
[19] |
M. Pernice and H. F. Walker, Nitsol: A newton iterative solver for nonlinear systems, SIAM J. Sci. Comput., 19 (1998), 302-318.
doi: 10.1137/S1064827596303843. |
[20] |
Y. Saad, "Iterative Methods for Sparse Linear Systems," 2nd edition, SIAM, Philadelphia, PA, 2003.
doi: 10.1137/1.9780898718003. |
[21] |
C. Sulem and P. L. Sulem, "The Nonlinear Schrödinger Equation, Self-focusing and Wave Collapse," Springer Verlag, New York, 1999. |
[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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