Robust Preconditioners for Saddle Point Problems
We survey preconditioning methods for matrices on saddle point form, as typically arising in constrained optimization problems. Special consideration is given to indefinite matrix preconditioners and a preconditioner which results in a symmetric positive definite matrix, which latter may enable the use of the standard conjugate gradient (CG) method. These methods result in eigenvalues with positive real parts and small or zero imaginary parts. The behaviour of some of these techniques is illustrated on solving a regularized Stokes problem.
KeywordsConjugate Gradient Method Preconditioned Conjugate Gradient Saddle Point Problem Unit Number Numerical Linear Algebra
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- 3.Axelsson O., Barker V.A., Neytcheva M., Polman B.: Solving the Stokes problem on a massively parallel computer. Mathematical Modelling and Analysis, 4 (2000), 1–22.Google Scholar
- 7.Axelsson O., Neytcheva M.: Preconditioning methods for linear systems arising in constrained optimization problems. Submitted to Numerical Linear Algebra with Applications, January 2002.Google Scholar
- 13.Ewing R.E., Lazarov R., Lu P., Vassilevski P.: Preconditioning indefinite systems arising from mixed finite element discretization of second order elliptic problems. In Axelsson O., Kolotilina L. (eds.): Lecture Notes in Mathematics, 1457, Springer-Verlag, Berlin, 1990.Google Scholar