Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems

O. Axelsson, J. Karátson

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)921-936
Number of pages16
JournalNumerical Functional Analysis and Optimization
Volume39
Issue number9
DOIs
Publication statusPublished - Jul 4 2018

    Fingerprint

Keywords

  • Optimal control
  • preconditioners
  • superlinear convergence

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

Cite this