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Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F

Year 2013, Volume: 10 Issue: 2, - , 01.11.2013

Azim Rivaz , Azita Tajaddini Asma Salarmohammadi

Abstract

In this paper, we present some convergence results of the extended global full
orthogonalization and the extended global generalized minimal residual methods. We also
present new expressions of the approximate solutions and the corresponding residuals.

Keywords

Extended block Krylov subspace Extended global FOM Extended global GMRES

References

  • R. Bouyouli, K. Jbilou, R. Sadaka, H. Sadok, Convergence properties of some block Krylov subspace methods for multiple linear systems, Journal of Computational and Applied Mathematics 196 (2006), 498-511.
  • F. Ding, T.Chen, Iterative least-squares solutions of coupled Sylvester matrix equations, Systems & Control Letters 54 (2005), 95-107.
  • F. Ding, T. Chen, On iterative solutions of general coupled matrix equations, SIAM Journal on Control and Optimization 44 (2006), 2269-2284.
  • F. Ding, P. X. Liu, J. Ding, Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle, Applied Mathematics and Computation 197 (2008), 41-50.
  • J. Ding, Y. Liu, F. Ting, Iterative solutions to matrix equations of the form Ai XBi =Fi , Computers and Mathematics with Applications 59 (2010), 3500-3507.
  • G. X. Haung, F. Yin, K. Guo, An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation AXB=C, Journal of Computational and Applied Mathematics 212 (2008), 231-244.
  • R. Lancaster, Theory of Matrix, Academic Press, New York, (1969).
  • A. Messaoudi, Recursive interpolation algorithm: a formalism for solving systems of linear equations—I. Direct methods, Journal of Computational and Applied Mathematics 76 (1996), 13-30.
  • F. Panjeh Ali Beik, Note to the global GMRES for solving the matrix equation AXB=F, International Journal of Engineering and Natural Sciences 5 (2011), 101-105.

Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F

Year 2013, Volume: 10 Issue: 2, - , 01.11.2013

Azim Rivaz , Azita Tajaddini Asma Salarmohammadi

Abstract

In this paper, we present some convergence results of the extended global full orthogonalization and the extended global generalized minimal residual methods. We also present new expressions of the approximate solutions and the corresponding residuals.

Keywords

Extended block Krylov subspace Extended global FOM Extended global GMRES

References

  • R. Bouyouli, K. Jbilou, R. Sadaka, H. Sadok, Convergence properties of some block Krylov subspace methods for multiple linear systems, Journal of Computational and Applied Mathematics 196 (2006), 498-511.
  • F. Ding, T.Chen, Iterative least-squares solutions of coupled Sylvester matrix equations, Systems & Control Letters 54 (2005), 95-107.
  • F. Ding, T. Chen, On iterative solutions of general coupled matrix equations, SIAM Journal on Control and Optimization 44 (2006), 2269-2284.
  • F. Ding, P. X. Liu, J. Ding, Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle, Applied Mathematics and Computation 197 (2008), 41-50.
  • J. Ding, Y. Liu, F. Ting, Iterative solutions to matrix equations of the form Ai XBi =Fi , Computers and Mathematics with Applications 59 (2010), 3500-3507.
  • G. X. Haung, F. Yin, K. Guo, An iterative method for the skew-symmetric solution and the optimal approximate solution of the matrix equation AXB=C, Journal of Computational and Applied Mathematics 212 (2008), 231-244.
  • R. Lancaster, Theory of Matrix, Academic Press, New York, (1969).
  • A. Messaoudi, Recursive interpolation algorithm: a formalism for solving systems of linear equations—I. Direct methods, Journal of Computational and Applied Mathematics 76 (1996), 13-30.
  • F. Panjeh Ali Beik, Note to the global GMRES for solving the matrix equation AXB=F, International Journal of Engineering and Natural Sciences 5 (2011), 101-105.
There are 9 citations in total.

Details

Subjects Engineering
Journal Section Articles
Authors

Azim Rivaz

Azita Tajaddini This is me

Asma Salarmohammadi This is me

Publication Date November 1, 2013
Published in Issue Year 2013 Volume: 10 Issue: 2

Cite

APA Rivaz, A., Tajaddini, A., & Salarmohammadi, A. (2013). Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F. Cankaya University Journal of Science and Engineering, 10(2).
AMA Rivaz A, Tajaddini A, Salarmohammadi A. Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F. CUJSE. November 2013;10(2).
Chicago Rivaz, Azim, Azita Tajaddini, and Asma Salarmohammadi. “Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F”. Cankaya University Journal of Science and Engineering 10, no. 2 (November 2013).
EndNote Rivaz A, Tajaddini A, Salarmohammadi A (November 1, 2013) Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F. Cankaya University Journal of Science and Engineering 10 2
IEEE A. Rivaz, A. Tajaddini, and A. Salarmohammadi, “Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F”, CUJSE, vol. 10, no. 2, 2013.
ISNAD Rivaz, Azim et al. “Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F”. Cankaya University Journal of Science and Engineering 10/2 (November 2013).
JAMA Rivaz A, Tajaddini A, Salarmohammadi A. Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F. CUJSE. 2013;10.
MLA Rivaz, Azim et al. “Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F”. Cankaya University Journal of Science and Engineering, vol. 10, no. 2, 2013.
Vancouver Rivaz A, Tajaddini A, Salarmohammadi A. Convergence Analysis of Extended Global FOM and Extended Global GMRES For Matrix Equations AXB = F. CUJSE. 2013;10(2).