Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6892378 | Computers & Mathematics with Applications | 2017 | 15 Pages |
Abstract
By using the Galerkin finite element method, the distributed control problems can be discretized into a saddle point problem with a coefficient matrix of block three-by-three, which can be reduced to a linear system with lower order. We first introduce a class of inexact block diagonal preconditioners and estimate the lower and upper bounds of positive and negative eigenvalues of the preconditioned matrices, respectively. Based on the Cholesky decomposition of the known matrices, we also analyze a lower triangular preconditioner to accelerate the minimal residual method for the reduced linear system and discuss its real and complex eigenvalues respectively. Moreover, these bounds do not rely on the regularization parameter and the eigenvalues of the matrices in the discrete system. Numerical experiments are also presented to demonstrate the effectiveness and robustness of the two new preconditioners.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Na Huang, Chang-Feng Ma,