Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6891974 | Computers & Mathematics with Applications | 2018 | 19 Pages |
Abstract
For the structured systems of linear equations arising from the Galerkin finite element discretizations of elliptic PDE-constrained optimization problems, some preconditioners are proposed to accelerate the convergence rate of Krylov subspace methods such as GMRES for both cases of the Tikhonov parameter β not very small (equal or greater than 1eâ6) and sufficiently small (less than 1eâ6), respectively. We derive the explicit expressions for the eigenvalues and eigenvectors of the corresponding preconditioned matrices. Numerical results show that the corresponding preconditioned GMRES methods perform and match well with the theoretical results.
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Authors
Yi-Fen Ke, Chang-Feng Ma,