A parameterized splitting iteration method for complex symmetric linear systems
In this paper, we propose a parameterized splitting (PS) iteration method for solving complex symmetric linear systems. The convergence theory of the method is established and the spectral properties of the corresponding iteration matrix are analyzed. The explicit expression for the spectral radius of the iteration matrix is given. In addition, the optimal choice of the iteration parameter is discussed. It is shown that the eigenvalues of the preconditioned matrix are cluster at 1. Numerical experiments illustrate the theoretical results and also examine the numerical effectiveness of the new parameterized splitting iteration method served either as a preconditioner or as a solver.
KeywordsComplex symmetric linear systems PMHSS iteration method GMRES Spectral properties Preconditioning
Mathematics Subject Classification (2000)65F08 65F10 65F50 65N22
Unable to display preview. Download preview PDF.
- 7.Bai, Z-Z., Benzi, M., Chen, F., Wang, Z.-Q.: Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with application to distributed control problems. IMA J. Numer. Anal. 33(1):343–369 (2013)Google Scholar
- 11.Betts, J.T.: Practical Methods For Optimal Control Using Nonlinear Programming. SIAM, Philadelphia, (2001)Google Scholar
- 13.Frommer, A., Lippert, T., Medeke, B., Schilling, K.: Numerical challenges in lattice quantum chromodynamics, Lecture notes in computational science and engineering. Springer, Heidelberg, 15 (2000)Google Scholar
- 15.van Dijk, W., Toyama, F.M.: Accurate numerical solutions of the time-dependent Schrodinger equation. Phys. Rev. E, 75, 036707 (2007)Google Scholar
- 16.Young, D.M.: Iterative Solution of Large Linear Systems. Academic Press, New York, (1971)Google Scholar