A Modified Preconditioner for Parameterized Inexact Uzawa Method for Indefinite Saddle Point Problems

Authors

  • Xinhui Shao Department of Mathematics, College of Science, Northeastern University, Shenyang, China
  • Chen Li Department of Mathematics, College of Science, Northeastern University, Shenyang, China
  • Tie Zhang Department of Mathematics, School of Information Science and Engineering, Northeastern University, Shenyang 110004, China
  • Changjun Li Department of Mathematics, College of Science, Northeastern University, Shenyang, China

DOI:

https://doi.org/10.4208/jcm.1702-m2016-0665

Keywords:

Preconditioner, Inexact Uzawa method, Saddle point problems, Indefiniteness, Convergence.

Abstract

The preconditioner for parameterized inexact Uzawa methods has been used to solve some indefinite saddle point problems. Firstly, we modify the preconditioner by making it more generalized, then we use theoretical analyses to show that the iteration method converges under certain conditions. Moreover, we discuss the optimal parameter and matrices based on these conditions. Finally, we propose two improved methods. Numerical experiments are provided to show the effectiveness of the modified preconditioner. All methods have fantastic convergence rates by choosing the optimal parameter and matrices.

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Published

2018-09-17

Issue

Vol. 36 No. 4 (2018)

Section

Articles