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Global Convergence of Algorithms Based on Unions of Non-Expansive Maps.
- Source :
-
Mathematics (2227-7390) . Jul2023, Vol. 11 Issue 14, p3213. 11p. - Publication Year :
- 2023
-
Abstract
- In his recent research, M. K. Tam (2018) considered a framework for the analysis of iterative algorithms which can be described in terms of a structured set-valued operator. At each point in the ambient space, the value of the operator can be expressed as a finite union of values of single-valued para-contracting operators. He showed that the associated fixed point iteration is locally convergent around strong fixed points. In the present paper we generalize the result of Tam and show the global convergence of his algorithm for an arbitrary starting point. An analogous result is also proven for the Krasnosel'skiāMann iterations. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NONEXPANSIVE mappings
*ALGORITHMS
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 11
- Issue :
- 14
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 169713246
- Full Text :
- https://doi.org/10.3390/math11143213