Preconditioners for reduced saddle point systems arising in elliptic PDE-constrained optimization problems
Yuping Zeng, Siqing Wang, Hongru Xu, Shuilian Xie · Journal of Inequalities and Applications · 2015
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.