论文信息 - The analysis of restart DGMRES for solving singular linear systems

The analysis of restart DGMRES for solving singular linear systems

Abstract A surprising phenomenon concerning with restart DGMRES [A. Sidi, DGMRES: a GMRES-type algorithm for Drazin-inverse solution of singular nonsymmetric linear systems, Linear Algebra Appl. 335 (2001) 189–204] is presented, that small values of the restart parameter may converge faster than larger values. We take three examples where DGMRES(2) converge, while DGMRES(3) stagnates to interpret the phenomenon. Two of these examples reveals that DGMRES convergence can be extremely sensitive to small changes in the initial residual.

Yimin Wei | Jieyong Zhou

[1] Hebing Wu,et al. Convergence properties of Krylov subspace methods for singular linear systems with arbitrary index , 2000 .

[2] Mark Embree,et al. The Tortoise and the Hare Restart GMRES , 2003, SIAM Rev..

[3] Yimin Wei,et al. Stagnation analysis of DGMRES , 2004, Appl. Math. Comput..

[4] Avram Sidi,et al. A unified approach to Krylov subspace methods for the Drazin-inverse solution of singular nonsymmetric linear systems , 1999 .

[5] Avram Sidi,et al. DGMRES: A GMRES-type algorithm for Drazin-inverse solution of singular non-symmetric linear systems , 2001 .

[6] Vladimir Kluzner,et al. A Bi-CG type iterative method for Drazin-inverse solution of singular inconsistent nonsymmetric linear systems of arbitrary index. , 1999 .

[7] Dianne P. O'Leary,et al. Complete stagnation of gmres , 2003 .

[8] Yimin Wei,et al. DFOM algorithm and error analysis for projection methods for solving singular linear system , 2004, Appl. Math. Comput..