A study of the influence of center conditions on the domain of parameters of Newton’s method by using recurrence relations

This paper focuses on the importance of center conditions on the first derivative of the operator involved in the solution of nonlinear equations by Newton’s method when the semilocal convergence of the method is established from the technique of recurrence relations.

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Bibliographic Details
Published in:	Advances in computational mathematics Vol. 43; no. 5; pp. 1103 - 1129
Main Authors:	Ezquerro, J. A., Hernández-Verón, M. A.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-10-2017 Springer Nature B.V
Subjects:	Computational mathematics Computational Mathematics and Numerical Analysis Computational Science and Engineering Mathematical and Computational Biology Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Nonlinear equations Visualization Semilocal convergence 47H99 Domain of parameters Nonlinear system Newton’s method 65H10 Recurrence relations 65J15
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Description
Summary:	This paper focuses on the importance of center conditions on the first derivative of the operator involved in the solution of nonlinear equations by Newton’s method when the semilocal convergence of the method is established from the technique of recurrence relations.
ISSN:	1019-7168 1572-9044
DOI:	10.1007/s10444-017-9518-z