Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems

0495405 - ÚGN 2019 RIV US eng J - Journal Article
Axelsson, Owe - Karátson, J.
Superlinear Convergence of the GMRES for PDE-Constrained Optimization Problems.
Numerical Functional Analysis and Optimization. Roč. 39, č. 9 (2018), s. 921-936. ISSN 0163-0563. E-ISSN 1532-2467
R&D Projects: GA MŠMT LQ1602
Institutional support: RVO:68145535
Keywords : optimal control * preconditioners * superlinear convergence
OECD category: Applied mathematics
Impact factor: 0.822, year: 2018
https://www.tandfonline.com/doi/full/10.1080/01630563.2018.1431928?scroll=top&needAccess=true

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.
Permanent Link: http://hdl.handle.net/11104/0288402