Super-attracting periodic orbits for a classical third order method

S. Amat; C. Bermúdez; S. Busquier; J. Carrasco; S. Plaza

doi:10.1016/j.cam.2006.08.032

Super-attracting periodic orbits for a classical third order method

S. Amat, C. Bermúdez, S. Busquier, J. Carrasco, S. Plaza

Research output: Contribution to journal › Article › peer-review

Abstract

We use a classical third order root-finding iterative method for approximating roots of nonlinear equations. We present a procedure for constructing polynomials so that super-attracting periodic orbits of any prescribed period occur when this method is applied. This note can be considered as the second part of our previous study [S. Amat, S. Busquier, S. Plaza, A construction of attracting periodic orbits for some classical third order iterative methods, J. Comput. Appl. Math. 189(1-2) (2006) 22-33]. © 2006 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	599-602
Number of pages	3
Journal	Journal of Computational and Applied Mathematics
Volume	206
Issue number	1
DOIs	https://doi.org/10.1016/j.cam.2006.08.032
Publication status	Published - 1 Sept 2007

Keywords

Attracting periodic orbits
Dynamics
Rational maps
Third order iterative method

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10.1016/j.cam.2006.08.032

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abstract = "We use a classical third order root-finding iterative method for approximating roots of nonlinear equations. We present a procedure for constructing polynomials so that super-attracting periodic orbits of any prescribed period occur when this method is applied. This note can be considered as the second part of our previous study [S. Amat, S. Busquier, S. Plaza, A construction of attracting periodic orbits for some classical third order iterative methods, J. Comput. Appl. Math. 189(1-2) (2006) 22-33]. {\textcopyright} 2006 Elsevier B.V. All rights reserved.",

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author = "S. Amat and C. Berm{\'u}dez and S. Busquier and J. Carrasco and S. Plaza",

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T1 - Super-attracting periodic orbits for a classical third order method

AU - Amat, S.

AU - Bermúdez, C.

AU - Busquier, S.

AU - Carrasco, J.

AU - Plaza, S.

PY - 2007/9/1

Y1 - 2007/9/1

N2 - We use a classical third order root-finding iterative method for approximating roots of nonlinear equations. We present a procedure for constructing polynomials so that super-attracting periodic orbits of any prescribed period occur when this method is applied. This note can be considered as the second part of our previous study [S. Amat, S. Busquier, S. Plaza, A construction of attracting periodic orbits for some classical third order iterative methods, J. Comput. Appl. Math. 189(1-2) (2006) 22-33]. © 2006 Elsevier B.V. All rights reserved.

AB - We use a classical third order root-finding iterative method for approximating roots of nonlinear equations. We present a procedure for constructing polynomials so that super-attracting periodic orbits of any prescribed period occur when this method is applied. This note can be considered as the second part of our previous study [S. Amat, S. Busquier, S. Plaza, A construction of attracting periodic orbits for some classical third order iterative methods, J. Comput. Appl. Math. 189(1-2) (2006) 22-33]. © 2006 Elsevier B.V. All rights reserved.

KW - Attracting periodic orbits

KW - Dynamics

KW - Rational maps

KW - Third order iterative method

U2 - 10.1016/j.cam.2006.08.032

DO - 10.1016/j.cam.2006.08.032

M3 - Article

SN - 0377-0427

VL - 206

SP - 599

EP - 602

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Super-attracting periodic orbits for a classical third order method

Abstract

Keywords

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