Termination criteria for inexact fixed-point schemes
(2015) In Numerical Linear Algebra with Applications 22(4). p.702-716- Abstract
- We analyze inexact fixed-point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed-point iteration. Important applications are the Picard iteration and partitioned fluid-structure interaction. For the analysis, the iteration is modeled as a perturbed fixed-point iteration, and existing analysis is extended to the nested case x=F(S(x)). We prove that if the iteration converges, it converges to the exact solution irrespective of the tolerance in the inner systems, provided that a nonstandard relative termination criterion is employed, whereas standard relative and absolute criteria do not have... (More)
- We analyze inexact fixed-point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed-point iteration. Important applications are the Picard iteration and partitioned fluid-structure interaction. For the analysis, the iteration is modeled as a perturbed fixed-point iteration, and existing analysis is extended to the nested case x=F(S(x)). We prove that if the iteration converges, it converges to the exact solution irrespective of the tolerance in the inner systems, provided that a nonstandard relative termination criterion is employed, whereas standard relative and absolute criteria do not have this property.
Numerical results demonstrate the effectiveness of the approach with the nonstandard termination criterion. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/5277077
- author
- Birken, Philipp LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- fixed-point iteration, Picard iteration, transmission problem, Dirichlet–Neumann iteration, termination criteria
- in
- Numerical Linear Algebra with Applications
- volume
- 22
- issue
- 4
- pages
- 702 - 716
- publisher
- Wiley-Blackwell
- external identifiers
-
- wos:000357833700007
- scopus:84935757636
- ISSN
- 1070-5325
- DOI
- 10.1002/nla.1982
- language
- English
- LU publication?
- yes
- additional info
- The information about affiliations in this record was updated in December 2015. The record was previously connected to the following departments: Numerical Analysis (011015004)
- id
- f26bdfeb-5fa8-4c67-aaf2-20ed9198902c (old id 5277077)
- date added to LUP
- 2016-04-01 10:42:33
- date last changed
- 2022-04-20 05:29:40
@article{f26bdfeb-5fa8-4c67-aaf2-20ed9198902c,
abstract = {{We analyze inexact fixed-point iterations where the generating function contains an inexact solve of an equation system to answer the question of how tolerances for the inner solves influence the iteration error of the outer fixed-point iteration. Important applications are the Picard iteration and partitioned fluid-structure interaction. For the analysis, the iteration is modeled as a perturbed fixed-point iteration, and existing analysis is extended to the nested case x=F(S(x)). We prove that if the iteration converges, it converges to the exact solution irrespective of the tolerance in the inner systems, provided that a nonstandard relative termination criterion is employed, whereas standard relative and absolute criteria do not have this property.<br/><br>
Numerical results demonstrate the effectiveness of the approach with the nonstandard termination criterion.}},
author = {{Birken, Philipp}},
issn = {{1070-5325}},
keywords = {{fixed-point iteration; Picard iteration; transmission problem; Dirichlet–Neumann iteration; termination criteria}},
language = {{eng}},
number = {{4}},
pages = {{702--716}},
publisher = {{Wiley-Blackwell}},
series = {{Numerical Linear Algebra with Applications}},
title = {{Termination criteria for inexact fixed-point schemes}},
url = {{http://dx.doi.org/10.1002/nla.1982}},
doi = {{10.1002/nla.1982}},
volume = {{22}},
year = {{2015}},
}