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

Involved external institutions

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