A Matching-Strategy-Inspired Preconditioning for Elliptic Optimal Control Problems

Chaojie Wang (), Jie Chen and Shuen Sun
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Chaojie Wang: School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
Jie Chen: School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
Shuen Sun: School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China

Mathematics, 2023, vol. 11, issue 12, 1-8

Abstract: 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.

Keywords: elliptic optimal control; linear system; preconditioning; Schur complement; GMRES method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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