Title :
A Preconditioned GMRES Method for Elliptic PDE-constrained Optimization Problems
Author :
Cong-Yi Zhu ; Yu-Mei Huang
Author_Institution :
Sch. of Math. & Stat., Lanzhou Univ., Lanzhou, China
Abstract :
In this paper, we consider the system of linear equations resulted from the elliptic PDE-constrained optimization distributed control problems. A new preconditioner is constructed and the preconditioned Generalized Minimum Residual (GMRES) method is applied to solve the linear system. Theoretical analysis and numerical experimental result show that the proposed preconditioned GMRES method is competitive to the existing preconditioned Krylov subspace methods appearing in the literature for this problem.
Keywords :
distributed control; elliptic equations; linear systems; optimisation; partial differential equations; elliptic PDE-constrained optimization distributed control problems; linear equation system; preconditioned GMRES method; preconditioned Krylov subspace methods; preconditioned generalized minimum residual method; Decentralized control; Educational institutions; Eigenvalues and eigenfunctions; Equations; Linear systems; Optimization; Symmetric matrices; distributed control problem; eigenvalues and eigenvectors; preconditioning matrix; spectral distribution; the GMRES method;
Conference_Titel :
Computational Intelligence and Security (CIS), 2014 Tenth International Conference on
Conference_Location :
Kunming
Print_ISBN :
978-1-4799-7433-7
DOI :
10.1109/CIS.2014.76
