Extending Global Full Orthogonalization method for Solving the Matrix Equation AXB=F
In the present work, we propose a new method for
solving the matrix equation AXB=F . The new method can
be considered as a generalized form of the well-known global full
orthogonalization method (Gl-FOM) for solving multiple linear
systems. Hence, the method will be called extended Gl-FOM (EGl-
FOM). For implementing EGl-FOM, generalized forms of block
Krylov subspace and global Arnoldi process are presented. Finally,
some numerical experiments are given to illustrate the efficiency of
our new method.
[1] R. Bouyouli, K. Jbilou, A. Messaoudi and H. Sadok, On block minimal
residual methods, Appl. Math. Lett, 20 (2007), 284-289.
[2] F. Ding, P. X. Liu and J. Ding, Iterative solutions of the generalized
Sylvester matrix equation by using hierarchical identification principle,
Appl. Math. Comput, 197 (2008), 41-50.
[3] A. El Guennouni, K. Jbilou and H. Sadok, A block version of BiCGSTAB
for linear systems with multiple right-hand sides, Trans. Numer. Anal,
16 (2003), 129-142.
[4] G. X. Huang, F. Yin, K. Guo, An iterative method for the skew-symmetric
solution and the optimal approximate solution of the matrix equation AXB
=C, J. Comput. Appl. Math, 212 (2008), 231-244.
[5] K. Jbilou, A. Messaoudi and H. Sadok, Global FOM and GMRES
algorithms for matrix equations, Appl. Numer. Math, 31 (1999), 43-
49.
[6] P. Lancaster. Theory of Matrix. Academic Press, New York, 1969.
[7] Y.-Q. Lin, Implicitly restarted global FOM and GMRES for nonsymmetric
matrix equations and Sylvester equations, Appl. Math. Comput, 167
(2005), 1004-1025.
[8] M. Mohseni Moghadam and F. Panjeh Ali Beik, A new weighted global
full orthogonalization method for solving nonsymmetric linear systems
with multiple right-hand sides, Int. Elect. J. Pure Appl. Math, 2(2)(2010),
47-67.
[9] M. Mohseni Moghadam and F. Panjeh Ali Beik, On a new weighted
global GMRES for solving nonsymmetric linear system with multiple
right-hand sides, Int. Journal of contemp. Math. Sciences, 5 (2010),
2237-2255.
[10] M. Mohseni Moghadam and F. Panjeh Ali Beik, A new weighted global
full orthogonalization method for shifted linear system with multiple
right-hand sides, Int. Math. Forum, 5 (2010), 2857-2874.
[11] Y. Saad, Iterative Methods for Sparse Linear System, PWS Press, New
York, 1995.
[12] M. Sadkane, Block Arnoldi and Davidson methods for unsymmetrical
large eigenvalue problems, Numer. Math, 64 (1993), 687-706.
[1] R. Bouyouli, K. Jbilou, A. Messaoudi and H. Sadok, On block minimal
residual methods, Appl. Math. Lett, 20 (2007), 284-289.
[2] F. Ding, P. X. Liu and J. Ding, Iterative solutions of the generalized
Sylvester matrix equation by using hierarchical identification principle,
Appl. Math. Comput, 197 (2008), 41-50.
[3] A. El Guennouni, K. Jbilou and H. Sadok, A block version of BiCGSTAB
for linear systems with multiple right-hand sides, Trans. Numer. Anal,
16 (2003), 129-142.
[4] G. X. Huang, F. Yin, K. Guo, An iterative method for the skew-symmetric
solution and the optimal approximate solution of the matrix equation AXB
=C, J. Comput. Appl. Math, 212 (2008), 231-244.
[5] K. Jbilou, A. Messaoudi and H. Sadok, Global FOM and GMRES
algorithms for matrix equations, Appl. Numer. Math, 31 (1999), 43-
49.
[6] P. Lancaster. Theory of Matrix. Academic Press, New York, 1969.
[7] Y.-Q. Lin, Implicitly restarted global FOM and GMRES for nonsymmetric
matrix equations and Sylvester equations, Appl. Math. Comput, 167
(2005), 1004-1025.
[8] M. Mohseni Moghadam and F. Panjeh Ali Beik, A new weighted global
full orthogonalization method for solving nonsymmetric linear systems
with multiple right-hand sides, Int. Elect. J. Pure Appl. Math, 2(2)(2010),
47-67.
[9] M. Mohseni Moghadam and F. Panjeh Ali Beik, On a new weighted
global GMRES for solving nonsymmetric linear system with multiple
right-hand sides, Int. Journal of contemp. Math. Sciences, 5 (2010),
2237-2255.
[10] M. Mohseni Moghadam and F. Panjeh Ali Beik, A new weighted global
full orthogonalization method for shifted linear system with multiple
right-hand sides, Int. Math. Forum, 5 (2010), 2857-2874.
[11] Y. Saad, Iterative Methods for Sparse Linear System, PWS Press, New
York, 1995.
[12] M. Sadkane, Block Arnoldi and Davidson methods for unsymmetrical
large eigenvalue problems, Numer. Math, 64 (1993), 687-706.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:60232", author = "Fatemeh Panjeh Ali Beik", title = "Extending Global Full Orthogonalization method for Solving the Matrix Equation AXB=F", abstract = "In the present work, we propose a new method for
solving the matrix equation AXB=F . The new method can
be considered as a generalized form of the well-known global full
orthogonalization method (Gl-FOM) for solving multiple linear
systems. Hence, the method will be called extended Gl-FOM (EGl-
FOM). For implementing EGl-FOM, generalized forms of block
Krylov subspace and global Arnoldi process are presented. Finally,
some numerical experiments are given to illustrate the efficiency of
our new method.", keywords = "Matrix equations, Iterative methods, Block Krylovsubspace methods.", volume = "5", number = "2", pages = "155-4", }