ON BLOCK PRECONDITIONERS FOR PDE-CONSTRAINED OPTIMIZATION PROBLEMS

作     者：Xiaoying Zhang Yumei Huang 

作者机构：School of Mathematics and Statistics Lanzhou University Lanzhou 730000 China 

出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)

年 卷 期：2014年第32卷第3期

页      面：272-283页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070105[理学-运筹学与控制论] 0714[理学-统计学（可授理学、经济学学位）] 070102[理学-计算数学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：国家自然科学基金 

主　　题：PDE-constrained optimization GMRES method Preconditioner Condition number Asymptotic convergence factor. 

摘      要：Recently, Bal proposed a block-counter-diagonal and a block-counter-triangular precon- ditioning matrices to precondition the GMRES method for solving the structured system of linear equations arising from the Galerkin finite-element discretizations of the distributed control problems in （Computing 91 （2011） 379-395）. He analyzed the spectral properties and derived explicit expressions of the eigenvalues and eigenvectors of the preconditioned matrices. By applying the special structures and properties of the eigenvector matrices of the preconditioned matrices, we derive upper bounds for the 2-norm condition numbers of the eigenvector matrices and give asymptotic convergence factors of the preconditioned GMRES methods with the block-counter-diagonal and the block-counter-triangular pre- conditioners. Experimental results show that the convergence analyses match well with the numerical results.