The Polynomial Pivots as Initial Values for a New Root‐Finding Iterative Method

Mario Lázaro, Pedro Martín, Antonio Agüero and Ignacio Ferrer

Journal of Applied Mathematics, 2015, vol. 2015, issue 1

Abstract: A new iterative method for polynomial root‐finding based on the development of two novel recursive functions is proposed. In addition, the concept of polynomial pivots associated with these functions is introduced. The pivots present the property of lying close to some of the roots under certain conditions; this closeness leads us to propose them as efficient starting points for the proposed iterative sequences. Conditions for local convergence are studied demonstrating that the new recursive sequences converge with linear velocity. Furthermore, an a priori checkable global convergence test inside pivots‐centered balls is proposed. In order to accelerate the convergence from linear to quadratic velocity, new recursive functions together with their associated sequences are constructed. Both the recursive functions (linear) and the corrected (quadratic convergence) are validated with two nontrivial numerical examples. In them, the efficiency of the pivots as starting points, the quadratic convergence of the proposed functions, and the validity of the theoretical results are visualized.

Date: 2015
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2015/413816

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:wly:jnljam:v:2015:y:2015:i:1:n:413816

Access Statistics for this article

More articles in Journal of Applied Mathematics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().