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Hybrid Newton-like Inverse Free Algorithms for Solving Nonlinear Equations.
- Source :
-
Algorithms . Apr2024, Vol. 17 Issue 4, p154. 17p. - Publication Year :
- 2024
-
Abstract
- Iterative algorithms requiring the computationally expensive in general inversion of linear operators are difficult to implement. This is the reason why hybrid Newton-like algorithms without inverses are developed in this paper to solve Banach space-valued nonlinear equations. The inverses of the linear operator are exchanged by a finite sum of fixed linear operators. Two types of convergence analysis are presented for these algorithms: the semilocal and the local. The Fréchet derivative of the operator on the equation is controlled by a majorant function. The semi-local analysis also relies on majorizing sequences. The celebrated contraction mapping principle is utilized to study the convergence of the Krasnoselskij-like algorithm. The numerical experimentation demonstrates that the new algorithms are essentially as effective but less expensive to implement. Although the new approach is demonstrated for Newton-like algorithms, it can be applied to other single-step, multistep, or multipoint algorithms using inverses of linear operators along the same lines. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 19994893
- Volume :
- 17
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Algorithms
- Publication Type :
- Academic Journal
- Accession number :
- 176878908
- Full Text :
- https://doi.org/10.3390/a17040154