GSTS-Uzawa method for a class of complex singular saddle point problems
- 94 Downloads
In this paper, we propose GSTS–Uzawa method for solving a class of complex singular saddle point problems based on generalized skew-Hermitian triangular splitting (GSTS) iteration method and classical Uzawa method. We research on its semi-convergence properties and the eigenvalues distributions of its preconditioned matrix. The resulting GSTS–Uzawa preconditioner is used to precondition Krylov subspace methods such as the restarted generalized minimal residual (GMRES) method for solving the equivalent formulation of the complex singular saddle point problems. The theoretical results and effectiveness of the GSTS–Uzawa method are supported by a numerical example.
KeywordsComplex singular saddle point problems GSTS-Uzawa method Iterative method Semi-convergence
Mathematics Subject Classification65F10 65F08
The authors would like to express our sincere thanks to the anonymous reviewers for their valuable suggestions which greatly improved the presentation of this paper. The authors are supported by the National Natural Science Foundation of China under Grant no. 61273311.
- Liesen J, de Sturler E, Sheffer A, Aydin Y, Siefert C (2001) Preconditioners for indefinite linear systems arising in surface parameterization. In: Proc. 10th international meshing round table, pp 71–81Google Scholar
- Yuan JY (1993) Iterative methods for generalized least squares problems. Ph.D. Thesis, IMPA, BrazilGoogle Scholar