Inexact inner-outer Golub-Kahan bidiagonalization method: A relaxation strategy
Darrigrand V, Dumitrasc A, Kruse C, Rüde U (2022)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2022
Journal
Journal Issue: e2484
URI: https://onlinelibrary.wiley.com/doi/10.1002/nla.2484
DOI: 10.1002/nla.2484
Open Access Link: https://onlinelibrary.wiley.com/doi/10.1002/nla.2484
Abstract
We study an inexact inner-outer generalized Golub-Kahan algorithm for the solution of saddle-point problems with a two-times-two block structure. In each outer iteration, an inner system has to be solved which in theory has to be done exactly. Whenever the system is getting large, an inner exact solver is, however, no longer efficient or even feasible and iterative methods must be used. We focus this article on a numerical study showing the influence of the accuracy of an inner iterative solution on the accuracy of the solution of the block system. Emphasis is further given on reducing the computational cost, which is defined as the total number of inner iterations. We develop relaxation techniques intended to dynamically change the inner tolerance for each outer iteration to further minimize the total number of inner iterations. We illustrate our findings on a Stokes problem and validate them on a mixed formulation of the Poisson problem.
Authors with CRIS profile
Andrei Dumitrasc
Lehrstuhl für Informatik 10 (Systemsimulation) (LSS)
Ulrich Rüde
Lehrstuhl für Informatik 10 (Systemsimulation) (LSS)
Involved external institutions
France (FR)How to cite
APA:
Darrigrand, V., Dumitrasc, A., Kruse, C., & Rüde, U. (2022). Inexact inner-outer Golub-Kahan bidiagonalization method: A relaxation strategy. Numerical Linear Algebra With Applications, e2484. https://doi.org/10.1002/nla.2484
MLA:
Darrigrand, Vincent, et al. "Inexact inner-outer Golub-Kahan bidiagonalization method: A relaxation strategy." Numerical Linear Algebra With Applications e2484 (2022).
BibTeX: Download