Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30685
Extending Global Full Orthogonalization method for Solving the Matrix Equation AXB=F

Authors: Fatemeh Panjeh Ali Beik

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: Iterative methods, Matrix equations, Block Krylovsubspace methods

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1076820

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1535

References:


[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.