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Preconditioned MHSS iteration methods for a class of block two-by-two linear systems with applications to distributed control problems. (English) Zbl 1271.65100

This paper introduces a preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration scheme suitable for solving and preconditioning a class of block two-by-two linear systems arising from the Galerkin finite element discretisations of a classs of distributed control problems. The authors analyze the convergence of this class of PMHSS iteration methods, and the spectral properties of PMHSS-preconditioned matrices. The PMHSS preconditioner is used to precondition Krylov subspace methods (MINRES and GMRES). The results are illustrated on several numerical experiments.

MSC:

65K10 Numerical optimization and variational techniques
65F08 Preconditioners for iterative methods
65F10 Iterative numerical methods for linear systems
49J20 Existence theories for optimal control problems involving partial differential equations
49M25 Discrete approximations in optimal control
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