References
- Bellalij , M. , Jbilou , K. and Sadok , H. 2008 . New convergence results on the global GMRES method for diagonalizable matrices . J. Comput. Appl. Math. , 219 : 350 – 358 . (doi:10.1016/j.cam.2007.09.016)
- Bouyouli , R. , Jbiloub , K. , Sadakac , R. and Sadok , H. 2006 . Convergence properties of some block Krylov subspace methods for multiple linear systems . J. Comput. Appl. Math. , 196 : 498 – 511 . (doi:10.1016/j.cam.2005.09.017)
- Bouyouli , R. , Jbilou , K. , Messaoudi , A. and Sadok , H. 2007 . On block minimal residual methods . Appl. Math. Lett. , 20 : 284 – 289 . (doi:10.1016/j.aml.2006.04.009)
- Gu , C.-Q. and Qian , H.-J. 2009 . Skew-symmetric methods for nonsymmetric linear systems with multiple right-hand sides . J. Comput. Appl. Math. , 223 : 567 – 577 . (doi:10.1016/j.cam.2008.01.001)
- Gu , K.-H. , Hu , X.-Y. and Zhang , L. 2007 . A new iteration method for the matrix equation AX=B . Appl. Math. Comput. , 187 : 1434 – 1441 . (doi:10.1016/j.amc.2006.08.153)
- Jbilou , K. 1999 . Smoothing iterative block methods for linear systems with multiple right-hand sides . J. Comput. Appl. Math. , 107 : 97 – 109 . (doi:10.1016/S0377-0427(99)00083-7)
- Jbilou , K. , Messaoudi , A. and Sadok , H. 1999 . Global FOM and GMRES algorithms for matrix equations . Appl. Numer. Math. , 31 : 49 – 63 . (doi:10.1016/S0168-9274(98)00094-4)
- Karimi , S. and Toutounian , F. 2006 . The block least squares method for solving nonsymmetric linear systems with multiple right-hand sides . Appl. Math. Comput. , 177 : 852 – 862 . (doi:10.1016/j.amc.2005.11.038)
- Ketabchi , S. and Salahi , M. 2009 . Correcting inconsistency in linear inequalities by minimal change in the right hand side vector . Comput. Sci. J. Moldova , 17 : 179 – 192 .
- Lei , Y. and Liao , A.-P. 2007 . A minimal residual algorithm for the inconsistent matrix equation AXB=C over symmetric matrices . Appl. Math. Comput. , 188 : 499 – 513 . (doi:10.1016/j.amc.2006.10.011)
- Li , F.-L. , Gong , L.-S. , Hu , X.-Y. and Zhang , L. 2010 . Successive projection iterative method for solving matrix equation AX=B . J. Comput. Appl. Math. , 234 : 2405 – 2410 . (doi:10.1016/j.cam.2010.03.008)
- Liao , A.-P. and Lei , Y. 2007 . Optimal approximate solution of the matrix equation AXB=C over symmetric matrices . J. Comput. Math. , 25 : 543 – 552 .
- Lin , Y.-Q. 2005 . Implicitly restarted global FOM and GMRES for nonsymmetric matrix equations and Sylvester equations . Appl. Math. Comput. , 167 : 1004 – 1025 . (doi:10.1016/j.amc.2004.06.141)
- Liu , Z.-Y. , Tian , Z.-L. and Tan , Y.-X. 2006 . Computing the least-square solutions for centrohermitian matrix problems . Appl. Math. Comput. , 174 : 566 – 577 . (doi:10.1016/j.amc.2005.04.104)
- Meng , C.-J. , Hu , X.-Y. and Zhang , L. 2005 . The skew-symmetric orthogonal solutions of the matrix equation AX=B . Linear Algebra Appl. , 402 : 303 – 318 . (doi:10.1016/j.laa.2005.01.022)
- Moreau , J.-J. 1962 . Décomposition orthogonale d'un espace hilbertien selon deux cones mutuellement polaires . C.R. Acad. Sci. Paris , 225 : 238 – 240 .
- Peng , Z.-Y. 2005 . An iterative method for the least squares symmetric solution of the linear matrix equation AXB=C . Appl. Math. Comput. , 170 : 711 – 723 . (doi:10.1016/j.amc.2004.12.032)
- Robbe , M. and Sadkane , M. 2006 . Exact and inexact breakdowns in the block GMRES Method . Linear Algebra Appl. , 419 : 265 – 285 . (doi:10.1016/j.laa.2006.04.018)
- Roger , A.-H. , Vladimir , S. and Naomi , S.-M. 2005 . Solution of linear matrix equations in a congruence class . Electron. J. Linear Algebra, , 13 : 153 – 156 .
- Salahi , M. and Ketabchi , S. 2010 . Correcting an inconsistent set of linear inequalities by generalized Newton method . Optim. Methods Softw. , 25 : 457 – 465 . (doi:10.1080/10556780903509531)
- Salkuyeh , D.-K. 2006 . CG-type algorithms to solve symmetric matrix equations . Appl. Math. Comput. , 172 : 985 – 999 . (doi:10.1016/j.amc.2005.03.003)
- Toutounian , F. and Karimi , S. 2006 . Global least squares method (Gl-LSQR) for solving general linear systems with several right-hand sides . Appl. Math. Comput. , 178 : 452 – 460 . (doi:10.1016/j.amc.2005.11.065)
- Trench , W.-F. 2004 . Hermitian, hermitian R-symmetric, and hermitian R-skew symmetric Procrustes problems . Linear Algebra Appl. , 387 : 83 – 98 . (doi:10.1016/j.laa.2004.01.018)
- Trench , W.-F. 2004 . Minimization problems for (R, S)-symmetric and (R, S)-skew symmetric matrices . Linear Algebra Appl. , 389 : 23 – 31 . (doi:10.1016/j.laa.2004.03.035)
- Wierzbicki , A.-P. and Kurcyusz , S. 1997 . Projection on a cone, penalty functionals and duality theory for problems with inequality constraints in Hilbert space . SIAM J. Control Optim. , 15 : 25 – 56 . (doi:10.1137/0315003)
- Xie , D.-X. , Sheng , Y. P. and Hu , X. Y. 2003 . The least-squares solutions of inconsistent matrix equation over symmetric and antipersymmetric matrices . Appl. Math. Lett. , 16 : 589 – 598 . (doi:10.1016/S0893-9659(03)00041-7)
- Xu , S.-F. 1998 . “ An Introduction to Inverse Algebraic Eigenvalue Problems ” . Beijing : Peking University Press .
- Zhang , J.-C. , Zhou , S.-Z. and Hu , X.-Y. 2009 . The (P,Q) generalized reflexive and anti-reflexive solutions of the matrix equation AX = B . Appl. Math. Comput. , 209 : 254 – 258 . (doi:10.1016/j.amc.2008.12.059)
- Zhao , L.-J. , Hu , X.-Y. and Zhang , L. 2008 . Least squares solutions to AX = B for bisymmetric matrices under a central principal submatrix constraint and the optimal approximation . Linear Algebra Appl. , 428 : 871 – 880 . (doi:10.1016/j.laa.2007.08.019)
- Zhou , S.-Q. and Dai , H. 1991 . “ Inverse Problem of Algebra Eigenvalue ” . Henan : Henan Science and Technology Press . (in Chinese)