March 2, 2012
Title: Numerical Solution of Saddle-Point Linear Systems
Abstract: Constrained partial differential equations and optimization problems typically require the need to solve special linear systems known as saddle-point systems. When the matrices are very large and sparse, iterative methods must be used. A challenge here is to derive and apply solution methods that exploit the properties and the structure of the given discrete operators, and yield fast convergence while imposing reasonable computer storage requirements. In this talk I will provide an overview of solution techniques. In particular, we will introduce and discuss effective preconditioners and their spectral properties, bounds on convergence rates, and computational challenges.