Improved Relaxed Positive-Definite and Skew-Hermitian Splitting Preconditioners for Saddle Point Problems

Authors

  • Yang Cao School of Transportation and Civil Engineering, Nantong University, Nantong 226019, P.R. China.
  • Zhiru Ren School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, China
  • Linquan Yao School of Urban Rail Transportation, Soochow University, Suzhou, 215006, China

DOI:

https://doi.org/10.4208/jcm.1710-m2017-0065

Keywords:

Saddle point problems, Preconditioning, RPSS preconditioner, Eigenvalues, Krylov subspace method.

Abstract

We establish a class of improved relaxed positive-definite and skew-Hermitian splitting (IRPSS) preconditioners for saddle point problems. These preconditioners are easier to be implemented than the relaxed positive-definite and skew-Hermitian splitting (RPSS) preconditioner at each step for solving the saddle point problem. We study spectral properties and the minimal polynomial of the IRPSS preconditioned saddle point matrix. A theoretical optimal IRPSS preconditioner is also obtained. Numerical results show that our proposed IRPSS preconditioners are superior to the existing ones in accelerating the convergence rate of the GMRES method for solving saddle point problems.

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Published

2018-08-23

Issue

Vol. 37 No. 1 (2019)

Section

Articles