Affine Iterations and Wrapping Effect: Various Approaches - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Acta Cybernetica Year : 2023

Affine Iterations and Wrapping Effect: Various Approaches

Itérations affines et effet enveloppant: différentes approches.

Abstract

Affine iterations of the form x(n+1) = Ax(n) + b converge, using real arithmetic, if the spectral radius of the matrix A is less than 1. However, substituting interval arithmetic to real arithmetic may lead to divergence of these iterations, in particular if the spectral radius of the absolute value of A is greater than 1. We will review different approaches to limit the overestimation of the iterates, when the components of the initial vector x(0) and b are intervals. We will compare, both theoretically and experimentally, the widths of the iterates computed by these different methods: the naive iteration, methods based on the QR-and SVD-factorization of A, and Lohner's QR-factorization method. The method based on the SVD-factorization is computationally less demanding and gives good results when the matrix is poorly scaled, it is superseded either by the naive iteration or by Lohner's method otherwise.
Fichier principal
Vignette du fichier
NRevol.pdf (755.79 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03505854 , version 1 (31-12-2021)

Licence

Attribution

Identifiers

Cite

Nathalie Revol. Affine Iterations and Wrapping Effect: Various Approaches. Acta Cybernetica, 2023, 26 (1), pp.129-147. ⟨10.14232/actacyb.295251⟩. ⟨hal-03505854⟩
76 View
31 Download

Altmetric

Share

Gmail Facebook X LinkedIn More