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Scaled relative graphs: nonexpansive operators via 2D Euclidean geometry.
- Source :
-
Mathematical Programming . Jul2022, Vol. 194 Issue 1/2, p569-619. 51p. - Publication Year :
- 2022
-
Abstract
- Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and nonexpansive fixed point iterations with a new tool called the scaled relative graph. The SRG provides a correspondence between nonlinear operators and subsets of the 2D plane. Under this framework, a geometric argument in the 2D plane becomes a rigorous proof of convergence. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00255610
- Volume :
- 194
- Issue :
- 1/2
- Database :
- Academic Search Index
- Journal :
- Mathematical Programming
- Publication Type :
- Academic Journal
- Accession number :
- 157667606
- Full Text :
- https://doi.org/10.1007/s10107-021-01639-w