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Mathematics, Vol. 11, Pages 2599: A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems
Mathematics doi: 10.3390/math11122599
Authors: Chaojie Wang Jie Chen Shuen Sun
In this paper, a new preconditioning method is proposed for the linear system arising from the elliptic optimal control problem. It is based on row permutations of the linear system and approximations of the corresponding Schur complement inspired by the matching strategy. The eigenvalue bounds of the preconditioned matrices are shown to be independent of mesh size and regularization parameter. Numerical results illustrate the efficiency of the proposed preconditioning methods.
