Block preconditioners for elliptic PDE-constrained optimization problems |
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Authors: | Zhong-Zhi Bai |
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Affiliation: | 1.School of Mathematics and Computer Science,Guizhou Normal University,Guiyang,People’s Republic of China;2.State Key Laboratory of Scientific/Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing,Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing,People’s Republic of China |
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Abstract: | For the structured systems of linear equations arising from the Galerkin finite-element discretizations of the distributed
control problems, we construct block-counter-diagonal and block-counter-tridiagonal preconditioning matrices to precondition
the Krylov subspace methods such as GMRES. We derive explicit expressions for the eigenvalues and eigenvectors of the corresponding
preconditioned matrices. Numerical implementations show that these structured preconditioners may lead to satisfactory experimental
results of the preconditioned GMRES methods when the regularization parameter is suitably small. |
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Keywords: | |
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