A multistep Steffensen‐type method for solving nonlinear systems of equations. (29th April 2019)

• Record Type: Journal Article
• Authors: Amat, Sergio; Argyros, Ioannis K.; Busquier, Sonia; Hernández‐Verón, Miguel A.; Magreñán, Á. Alberto; Martínez, Eulalia
• Other Names: Simos Theodore guestEditor.
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 13(2020)
• Page Start: 7518
• Page End: 7536
• Publication Date: 2019-04-29
• Subjects: frozen divided differences -- high‐order -- semilocal convergence -- Steffensen‐type methods; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5599
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper is devoted to the semilocal analysis of a high‐order Steffensen‐type method with frozen divided differences. The methods are free of bilinear operators and derivatives, which constitutes the main limitation of the classical high‐order iterative schemes. Although the methods are more demanding, a semilocal convergence analysis is presented using weaker conditions than the classical Steffensen method.