Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems. (4th July 2018) - Axelsson, O.; Karátson, J.
ABSTRACT: Optimal control problems for PDEs arise in many important applications. A main step in the solution process is the solution of the arising linear system, where the crucial point is usually finding a proper preconditioner. We propose both proper block diagonal and more involved preconditioners, and derive mesh independent superlinear convergence of the preconditioned GMRES iterations based on a compact perturbation property of the underlying operators.