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Numerische Mathematik

, Volume 93, Issue 2, pp 333–359 | Cite as

Two new variants of nonlinear inexact Uzawa algorithms for saddle-point problems

  • Qiya Hu
  • Jun Zou
Original article

Summary.

In this paper, we consider some nonlinear inexact Uzawa methods for iteratively solving linear saddle-point problems. By means of a new technique, we first give an essential improvement on the convergence results of Bramble-Paschiak-Vassilev for a known nonlinear inexact Uzawa algorithm. Then we propose two new algorithms, which can be viewed as a combination of the known nonlinear inexact Uzawa method with the classical steepest descent method and conjugate gradient method respectively. The two new algorithms converge under very practical conditions and do not require any apriori estimates on the minimal and maximal eigenvalues of the preconditioned systems involved, including the preconditioned Schur complement. Numerical results of the algorithms applied for the Stokes problem and a purely linear system of algebraic equations are presented to show the efficiency of the algorithms.

Mathematics Subject Classification: 65F10, 65N20 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Qiya Hu
    • 1
  • Jun Zou
    • 2
  1. 1.Institute of Computational Mathematics and Scientific Engineering Computing, Chinese Academy of Sciences, Beijing 100080, People's Republic of China; e-mail: hqy@lsec.cc.ac.cn CN
  2. 2.Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, People's Republic of China; e-mail: zou@math.cuhk.edu.hk HK

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