Affine iterations and wrapping effect various approaches /
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...
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| Dokumentumtípus: | Cikk |
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University of Szeged, Institute of Informatics
Szeged
2023
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| Sorozat: | Acta cybernetica
26 No. 1 |
| Kulcsszavak: | Intervallum analízis, Numerikus analízis, Affine iterációk |
| Tárgyszavak: | |
| doi: | 10.14232/actacyb.295251 |
| Online Access: | http://acta.bibl.u-szeged.hu/86969 |
| Tartalmi kivonat: | 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the SVD-factorization is computationally less demanding and gives good results when the matrix is poorly scaled, it is superseded either by the naive iteration or by Lohner's method otherwise. |
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| Terjedelem/Fizikai jellemzők: | 129-147 |
| ISSN: | 2676-993X |