Preconditioners for reduced saddle point systems arising in elliptic PDE-constrained optimization problems

摘要

In this paper, we propose some preconditioning techniques for reduced saddle point systems arising from linear elliptic distributed optimal control problems. The eigenvalues of preconditioned matrices are analyzed. Moreover, the bounds of these eigenvalues with respect to the mesh size h are also obtained. Some numerical tests are presented to validate the theoretical analysis.