Two-step AOR iteration method for the linear matrix equation \(AXB=C\). (English) Zbl 1476.65063
Summary: We propose a two-step AOR iteration method for solving the linear matrix equation \(AXB=C\). The convergence of this iteration method is discussed, and numerical results are reported to show the correctness of the theory and the effectiveness of this method.
References:
| [1] | Bai, Z-Z, Sharp error bounds of some Krylov subspace methods for non-Hermitian linear systems, Appl Math Comput, 109, 273-285 (2000) · Zbl 1026.65028 |
| [2] | Bai, Z-Z, On Hermitian and skew-Hermitian splitting iteration methods for the continuous Sylvester equations, J Comput Math, 29, 185-198 (2011) · Zbl 1249.65090 · doi:10.4208/jcm.1009-m3152 |
| [3] | Bai, Z-Z, Motivations and realizations of Krylov subspace methods for large sparse linear systems, J Comput Appl Math, 283, 71-78 (2015) · Zbl 1311.65032 · doi:10.1016/j.cam.2015.01.025 |
| [4] | 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, 24, 603-626 (2003) · Zbl 1036.65032 · doi:10.1137/S0895479801395458 |
| [5] | Deng, Y-B; Bai, Z-Z; Gao, Y-H, Iterative orthogonal direction methods for Hermitian minimum norm solutions of two consistent matrix equations, Num Linear Algebra Appl, 13, 801-823 (2006) · Zbl 1174.65382 · doi:10.1002/nla.496 |
| [6] | Fausett, DW; Fulton, CT, Large least squares problems involving Kronecker products, SIAM J Matrix Anal Appl, 15, 219-227 (1994) · Zbl 0798.65059 · doi:10.1137/S0895479891222106 |
| [7] | Golub, GH; Van Loan, CF, Matrix Computations (2013), Baltimore: The Johns Hopkins University Press, Baltimore · Zbl 1268.65037 |
| [8] | Li, X.; Huo, H-F; Yang, A-L, Preconditioned HSS iteration method and its non-alternating variant for continuous Sylvester equations, Comput Math Appl, 75, 1095-1106 (2018) · Zbl 1409.65027 · doi:10.1016/j.camwa.2017.10.028 |
| [9] | Liao, A-P; Bai, Z-Z, Least-squares solution of \(AXB=D\) over symmetric positive semidefinite matrices \(X\), J Comput Math, 21, 175-182 (2003) · Zbl 1029.65042 |
| [10] | Liao, A-P; Bai, Z-Z, Least squares symmetric and skew-symmetric solutions of the matrix equation \(AXA^T + BYB^T = C\) with the least norm, Math Num Sin, 27, 81-95 (2005) · Zbl 1099.65523 |
| [11] | Liu, Z-Y; Zhou, Y.; Zhang, Y-L; Lin, L.; Xie, D-X, Some remarks on Jacobi and Gauss-Seidel-type iteration methods for the matrix equation \(AXB = C\), Appl Math Comput, 354, 305-307 (2019) · Zbl 1429.65089 |
| [12] | Peng, Z-Y, An iterative method for the least squares symmetric solution of the linear matrix equation \(AXB=C\), Appl Math Comput, 170, 711-723 (2005) · Zbl 1081.65039 |
| [13] | Rauhala, UA, Introduction to array algebra, Photogramm Eng Remote Sens, 46, 177-192 (1980) |
| [14] | Regalia, PA; Mitra, SK, Kronecker products, unitary matrices and signal processing applications, SIAM Rev, 31, 586-613 (1989) · Zbl 0687.15010 · doi:10.1137/1031127 |
| [15] | Tian, Z-L; Tian, M-Y; Liu, Z-Y; Xu, T-Y, The Jacobi and Gauss-Seidel-type iteration methods for the matrix equation \(AXB=C\), Appl Math Comput, 292, 63-75 (2017) · Zbl 1410.65126 |
| [16] | Wang, X.; Li, Y.; Dai, L., On Hermitian and skew-Hermitian splitting iteration methods for the linear matrix equation \(AXB=C\), Comput Math Appl, 65, 657-664 (2013) · Zbl 1319.65033 · doi:10.1016/j.camwa.2012.11.010 |
| [17] | Yang, J.; Deng, Y-B, On the solutions of the equation \(AXB=C\) under Toeplitz-like and Hankel matrices constraint, Math Methods Appl Sci, 41, 2074-2094 (2018) · Zbl 1391.65114 · doi:10.1002/mma.4735 |
| [18] | Zak, MK; Toutounian, F., Nested splitting conjugate gradient method for matrix equation \(AXB=C\) and preconditioning, Comput Math Appl, 66, 269-278 (2013) · Zbl 1347.65078 · doi:10.1016/j.camwa.2013.05.004 |
| [19] | Zha, H., Comments on large least squares problems involving Kronecker products, SIAM J Matrix Anal Appl, 16, 1172 (1995) · Zbl 0834.65029 · doi:10.1137/S0895479894265009 |
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