Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems. (4th July 2018)

• Record Type: Journal Article
• Authors: Axelsson, O.; Karátson, J.
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 9(2018)
• Page Start: 921
• Page End: 936
• Publication Date: 2018-07-04
• Subjects: Optimal control -- preconditioners -- superlinear convergence; 65N30; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2018.1431928
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Optimal control problems for PDEs arise in many important applications. A main step in the solution process is the solution of the arising linear system, where the crucial point is usually finding a proper preconditioner. We propose both proper block diagonal and more involved preconditioners, and derive mesh independent superlinear convergence of the preconditioned GMRES iterations based on a compact perturbation property of the underlying operators.