Name
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 1e−6) and sufficiently small (less than 1e−6), 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. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.camwa.2018.01.009 | Computers & Mathematics with Applications |
Keywords | Field | DocType |
PDE-constrained optimization,Saddle point matrix,Preconditioner,Eigenvalue,Eigenvector | Tikhonov regularization,Krylov subspace,Generalized minimal residual method,Matrix (mathematics),Mathematical analysis,Finite element method,Rate of convergence,Optimization problem,Mathematics,Eigenvalues and eigenvectors | Journal |
Volume | Issue | ISSN |
75 | 8 | 0898-1221 |
Citations | PageRank | References |
1 | 0.36 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yi-Fen Ke | 1 | 16 | 1.97 |
| Changfeng Ma | 2 | 100 | 16.25 |