On a Newton-Kurchatov-type Iterative Process. (2nd January 2016)

• Record Type: Journal Article
• Authors: Hernández-Verón, M. A.; Rubio, M. J.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 1(2016)
• Page Start: 65
• Page End: 79
• Publication Date: 2016-01-02
• Subjects: Kurchatov method -- Newton-Kantorovich method -- nondifferentiable operator -- semilocal convergence; 47H17 -- 65J15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2015.1084318
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: Newton's method and Kurchatov's method are iterative processes known for their fast speed of convergence. We construct from both methods an iterative method to approximate solutions of nonlinear equations given by a nondifferentiable operator, and we study its semilocal convergence in Banach spaces. Finally, we consider several applications of this new iterative process.