The rate of multiplicity of the roots of nonlinear equations and its application to iterative methods

V. Candela and R. Peris

Applied Mathematics and Computation, 2015, vol. 264, issue C, 417-430

Abstract: Nonsimple roots of nonlinear equations present some challenges for classic iterative methods, such as instability or slow, if any, convergence. As a consequence, they require a greater computational cost, depending on the knowledge of the order of multiplicity of the roots. In this paper, we introduce dimensionless function, called rate of multiplicity, which estimates the order of multiplicity of the roots, as a dynamic global concept, in order to accelerate iterative processes. This rate works not only with integer but also fractional order of multiplicity and even with poles (negative order of multiplicity).

Keywords: Iterative methods; Nonlinear equations; Rate of multiplicity; Nonsimple roots; Order of convergence; Stability (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300315005548
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:264:y:2015:i:c:p:417-430

DOI: 10.1016/j.amc.2015.04.092

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().