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The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method
Joint Authors
Lázaro, Mario
Martín, Pedro
Agüero, Antonio
Ferrer, Ignacio
Source
Journal of Applied Mathematics
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-14, 14 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-23
Country of Publication
Egypt
No. of Pages
14
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Lázaro, Mario& Martín, Pedro& Agüero, Antonio& Ferrer, Ignacio. 2015. The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method. Journal of Applied Mathematics،Vol. 2015, no. 2015, pp.1-14.
https://search.emarefa.net/detail/BIM-1067087
Modern Language Association (MLA)
Lázaro, Mario…[et al.]. The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method. Journal of Applied Mathematics No. 2015 (2015), pp.1-14.
https://search.emarefa.net/detail/BIM-1067087
American Medical Association (AMA)
Lázaro, Mario& Martín, Pedro& Agüero, Antonio& Ferrer, Ignacio. The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method. Journal of Applied Mathematics. 2015. Vol. 2015, no. 2015, pp.1-14.
https://search.emarefa.net/detail/BIM-1067087
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1067087