The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method
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 con...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/413816 |
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| author | Mario Lázaro Pedro Martín Antonio Agüero Ignacio Ferrer |
| author_facet | Mario Lázaro Pedro Martín Antonio Agüero Ignacio Ferrer |
| author_sort | Mario Lázaro |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-de77f51df8d14b1aacbcc0a25565a9e8 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-de77f51df8d14b1aacbcc0a25565a9e82025-02-03T05:46:09ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/413816413816The Polynomial Pivots as Initial Values for a New Root-Finding Iterative MethodMario Lázaro0Pedro Martín1Antonio Agüero2Ignacio Ferrer3Department of Continuum Mechanics and Theory of Structures, Universitat Politècnica de València, 46022 Valencia, SpainDepartment of Continuum Mechanics and Theory of Structures, Universitat Politècnica de València, 46022 Valencia, SpainDepartment of Continuum Mechanics and Theory of Structures, Universitat Politècnica de València, 46022 Valencia, SpainDepartment of Continuum Mechanics and Theory of Structures, Universitat Politècnica de València, 46022 Valencia, SpainA 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.http://dx.doi.org/10.1155/2015/413816 |
| spellingShingle | Mario Lázaro Pedro Martín Antonio Agüero Ignacio Ferrer The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method Journal of Applied Mathematics |
| title | The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method |
| title_full | The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method |
| title_fullStr | The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method |
| title_full_unstemmed | The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method |
| title_short | The Polynomial Pivots as Initial Values for a New Root-Finding Iterative Method |
| title_sort | polynomial pivots as initial values for a new root finding iterative method |
| url | http://dx.doi.org/10.1155/2015/413816 |
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