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Prize Lectures
Numerical Solution of Saddle-Point Systems
Saddle-point linear systems arise in many applications, mainly in problems that involve constraints. When the matrix is large and sparse, iterative methods must be used. State-of-the-art Krylov subspace methods are particularly effective, and they typically require the design of effective preconditioners. In this talk I will describe these linear systems, their mathematical and numerical properties, and preconditioned iterative methods for solving them. We will focus on a couple of elliptic PDEs that lead to those linear systems and present a few linear algebra results that help design effective solvers.