The Mathematical Institute, University of Oxford, Eprints Archive

Natural preconditioners for saddle point systems

Pestana, Jennifer and Wathen, A. J. (2013) Natural preconditioners for saddle point systems. Technical Report. Unspecified. (Submitted)

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Abstract

The solution of quadratic or locally quadratic extremum problems subject to linear(ized) constraints gives rise to linear systems in saddle point form. This is true whether in the continuous or discrete setting, so saddle point systems arising from discretization of partial differential equation problems such as those describing electromagnetic problems or incompressible flow lead to equations with this structure as does, for example, the widely used sequential quadratic programming approach to nonlinear optimization.
This article concerns iterative solution methods for these problems and in particular shows how the problem formulation leads to natural preconditioners which guarantee rapid convergence of the relevant iterative methods. These preconditioners are related to the original extremum problem and their effectiveness -- in terms of rapidity of convergence -- is established here via a proof of general bounds on the eigenvalues of the preconditioned saddle point matrix on which iteration convergence depends.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1754
Deposited By: Lotti Ekert
Deposited On:10 Oct 2013 08:07
Last Modified:29 May 2015 19:27

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