Optimization of extrapolated Cayley transform with non-Hermitian positive definite matrix
Tóm tắt
Từ khóa
Tài liệu tham khảo
Axelsson, 1994
Axelsson, 2013
Bai, 2007, Splitting iteration methods for non-Hermitian positive definite systems of linear equations, Hokkaido Math. J., 36, 801, 10.14492/hokmj/1272848034
Bai, 2009, Optimal parameters in the HSS-like methods for saddle-point problems, Numer. Linear Algebra Appl., 16, 447, 10.1002/nla.626
Bai, 2010, On semi-convergence of Hermitian and skew-Hermitian splitting methods for singular linear systems, Computing, 89, 171, 10.1007/s00607-010-0101-4
Bai, 2010, Modulus-based matrix splitting iteration methods for linear complementarity problems, Numer. Linear Algebra Appl., 17, 917, 10.1002/nla.680
Bai, 2012, Block alternating splitting implicit iteration methods for saddle-point problems from time-harmonic eddy current models, Numer. Linear Algebra Appl., 19, 914, 10.1002/nla.810
Bai, 2010, Modified HSS iteration methods for a class of complex symmetric linear systems, Computing, 87, 93, 10.1007/s00607-010-0077-0
Bai, 2007, Accelerated Hermitian and skew-Hermitian splitting iteration methods for saddle-point problems, IMA J. Numer. Anal., 27, 1, 10.1093/imanum/drl017
Bai, 2006, Optimal parameter in Hermitian and skew-Hermitian splitting method for certain two-by-two block matrices, SIAM J. Sci. Comput., 28, 583, 10.1137/050623644
Bai, 2007, Convergence properties of preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite matrices, Math. Comp., 76, 287, 10.1090/S0025-5718-06-01892-8
Bai, 2005, Block triangular and skew-Hermitian splitting methods for positive-definite linear systems, SIAM J. Sci. Comput., 26, 844, 10.1137/S1064827503428114
Bai, 2003, Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems, SIAM J. Matrix Anal. Appl., 24, 603, 10.1137/S0895479801395458
Bai, 2007, On successive overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations, Numer. Linear Algebra Appl., 14, 319, 10.1002/nla.517
Bai, 2004, Preconditioned Hermitian and skew-Hermitian splitting methods for non-Hermitian positive semidefinite linear systems, Numer. Math., 98, 1, 10.1007/s00211-004-0521-1
Bai, 2006, Alternately linearized implicit iteration methods for the minimal nonnegative solutions of the nonsymmetric algebraic Riccati equations, Numer. Linear Algebra Appl., 13, 655, 10.1002/nla.500
Bai, 2006, Two-step iterative methods for solving the stationary convection–diffusion equation with a small parameter at the highest derivative on a uniform grid, Comput. Math. Math. Phys., 46, 282, 10.1134/S0965542506020102
Bai, 2006, A shift-splitting preconditioner for non-Hermitian positive definite matrices, J. Comput. Math., 24, 539
Benzi, 2009, A generalization of the Hermitian and skew-Hermitian splitting iteration, SIAM J. Matrix Anal. Appl., 31, 360, 10.1137/080723181
Benzi, 2011, A dimensional split preconditioner for Stokes and linearized Navier–Stokes equations, Appl. Numer. Math., 61, 66, 10.1016/j.apnum.2010.08.005
Bertaccini, 2005, Preconditioned HSS methods for the solution of non-Hermitian positive definite linear systems and applications to the discrete convection–diffusion equation, Numer. Math., 99, 441, 10.1007/s00211-004-0574-1
van Bokhoven, 1981
Chiang, 2010, A structured doubling algorithm for discrete-time algebraic Riccati equations with singular control weighting matrices, Taiwanese J. Math., 14, 933, 10.11650/twjm/1500405875
Chikina, 2003, Solution of linear equation systems with a dominant skew-symmetric part using the product triangular iterative method, Comput. Methods Appl. Math., 3, 647, 10.2478/cmam-2003-0040
Coxeter, 1989
Deift, 1983, Ordinary differential equations and the symmetric eigenvalue problem, SIAM J. Numer. Anal., 20, 1, 10.1137/0720001
Diele, 1998, The Cayley transform in the numerical solution of unitary differential systems, Adv. Comput. Math., 8, 317, 10.1023/A:1018908700358
Dong, 2009, A modified modulus method for symmetric positive-definite linear complementarity problems, Numer. Linear Algebra Appl., 16, 129, 10.1002/nla.609
Elman, 1990, Iterative methods for cyclically reduced non-self-adjoint linear systems, Math. Comp., 54, 671
Elman, 1991, Iterative methods for cyclically reduced non-self-adjoint linear systems II, Math. Comp., 56, 215
Fallat, 2002, On the Cayley transform of positivity classes of matrices, Electron. J. Linear Algebra, 9, 190, 10.13001/1081-3810.1086
Gao, 2011, On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations, Numer. Linear Algebra Appl., 18, 325, 10.1002/nla.727
Greif, 1998, Iterative solution of cyclically reduced systems arising from discretization of the three-dimensional convection–diffusion equation, SIAM J. Sci. Comput., 19, 1918, 10.1137/S1064827596296994
Greif, 1999, Block stationary methods for nonsymmetric cyclically reduced systems arising from three-dimensional elliptic equations, SIAM J. Matrix Anal. Appl., 20, 1038, 10.1137/S0895479897317715
Guo, 2006, A structure-preserving doubling algorithm for nonsymmetric algebraic Riccati equation, Numer. Math., 103, 393, 10.1007/s00211-005-0673-7
Hadjidimos, 2007, Stationary biparametric ADI preconditioners for conjugate gradient methods, J. Comput. Appl. Math., 205, 364, 10.1016/j.cam.2006.05.033
Hadjidimos, 2012, On iterative solution for linear complementarity problem with an H+-matrix, SIAM J. Matrix Anal. Appl., 33, 97, 10.1137/100811222
Hadjidimos, 2008, The principle of extrapolation and the Cayley transform, Linear Algebra Appl., 429, 2465, 10.1016/j.laa.2007.10.021
Hadjidimos, 2009, On the optimal complex extrapolation of the complex Cayley transform, Linear Algebra Appl., 430, 619, 10.1016/j.laa.2008.08.010
Hadjidimos, 2009, Nonstationary extrapolated modulus algorithms for the solution of the linear complementarity problem, Linear Algebra Appl., 431, 197, 10.1016/j.laa.2009.02.024
Hassibi, 2002, Cayley differential unitary space–time codes, IEEE Trans. Inform. Theory, 48, 1485, 10.1109/TIT.2002.1003836
Hochwald, 2000, Unitary space–time modulation for multiple-antenna communication in Rayleigh flat-fading, IEEE Trans. Inform. Theory, 46, 543, 10.1109/18.825818
Huang, 2009, Structured doubling algorithms for weakly stabilizing Hermitian solutions of algebraic Riccati equations, Linear Algebra Appl., 430, 1452, 10.1016/j.laa.2007.08.043
Iserles, 2001, On Cayley-transform methods for the discretization of Lie-group equations, Found. Comput. Math., 1, 129, 10.1007/s102080010003
Jing, 2003, Unitary space–time modulation via Cayley transform, IEEE Trans. Signal Process., 51, 2891, 10.1109/TSP.2003.818202
Johnson, 2009, General resolution of a convergence question of L. Krukier, Numer. Linear Algebra Appl., 16, 949, 10.1002/nla.681
Kappel, 1986, Iterative algorithms for the linear complementarity problem, Int. J. Comput. Math., 19, 273, 10.1080/00207168608803522
Kellogg, 1963, Another alternating-direction-implicit method, J. Soc. Ind. Appl. Math., 11, 976, 10.1137/0111071
Krishnaprasad, 2001, Cayley transforms in micromagnetics, Phys. B, 306, 195, 10.1016/S0921-4526(01)01003-1
Krukier, 2002, Triangular skew-symmetric iterative solvers for strongly nonsymmetric positive real linear system of equations, Appl. Numer. Math., 41, 89, 10.1016/S0168-9274(01)00112-X
Krukier, 2009, Product-type skew-Hermitian triangular splitting iteration methods for strongly non-Hermitian positive definite linear systems, J. Comput. Appl. Math., 232, 3, 10.1016/j.cam.2008.10.033
Leenaerts, 1998
Lewis, 1994, Conserving algorithms for the dynamics of Hamiltonian systems on Lie groups, J. Nonlinear Sci., 4, 253, 10.1007/BF02430634
Lin, 2006, Convergence analysis of structure-preserving doubling algorithms for Riccati-type matrix equations, SIAM J. Matrix Anal. Appl., 28, 26, 10.1137/040617650
Marchuk, 1973
Meerbergen, 1994, Shift-invert and Cayley transforms for detection of rightmost eigenvalues of nonsymmetric matrices, BIT, 34, 409, 10.1007/BF01935650
Murty, 1988
Peaceman, 1955, The numerical solution of parabolic and elliptic differential equations, J. Soc. Ind. Appl. Math., 3, 28, 10.1137/0103003
Silverman, 1967
Wang, 2004, Skew-Hermitian triangular splitting iteration methods for non-Hermitian positive definite linear systems of strong skew-Hermitian parts, BIT, 44, 363, 10.1023/B:BITN.0000039428.54019.15
Yang, 2012, Bi-parameter incremental unknowns ADI iterative methods for elliptic problems, Numer. Algorithms, 60, 483, 10.1007/s11075-011-9525-y
Zanna, 1999, Collocation and relaxed collocation for the FER and the Magnus expansions, SIAM J. Numer. Anal., 36, 1145, 10.1137/S0036142997326616