C. María Concepción Bermúdez

C. María Concepción Bermúdez
Universidad Politécnica de Cartagena | UPCT · Departmetn of Applied Mathematics and Statistics

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9
Publications
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128
Citations
Citations since 2016
0 Research Items
64 Citations
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2016201720182019202020212022051015
Introduction

Publications

Publications (9)
Article
We study a general class of high order Newton type methods. The schemes consist of the application of several steps of Newton type methods with frozen derivatives. We are interested to improve the order of convergence in each sub-step. In particular, we should finish the computation after some stop criteria and before the full computation of the cu...
Article
Full-text available
This paper is devoted to the study of a class of high-order iterative methods for nonlinear equations on Banach spaces. An analysis of the convergence under Kantorovich-type conditions is proposed. Some numerical experiments, where the analyzed methods present better behavior than some classical schemes, are presented. These applications include th...
Article
A modification of some classical third order methods is studied. The main advantage of these methods is that they do not need evaluate any Frechet derivative. A convergence theorem in Banach spaces, just assuming that the second divided difference is bounded by a nondecreasing function and a punctual condition, is presented. Frechet differentiabili...
Article
The dynamics of a family of Newton's type iterative methods for second- and third-degree complex polynomials is studied. The conjugacy classes of these methods are presented. Classical properties of rational maps are used.
Article
This paper is devoted to the study of a third-order Newton-type method. The method is free of bilinear operators, which constitutes the main limitation of the classical third-order iterative schemes. First, a global convergence theorem in the real case is presented. Second, a semilocal convergence theorem and some examples are analyzed, including q...
Article
The dynamics of Euler’s third-order iterative method which is used to find roots of non-linear equations applied to complex polynomials of degrees three and four is studied. The conjugacy classes of this method are found explicitly.
Article
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. Busqui...
Article
We use the nondiscrete mathematical induction method for the semi-local convergence of a two step secant's iterative scheme on a Banach space. The scheme does not need to evaluate neither any Fréchet derivative nor any bilinear operator, but having a high speed of convergence.

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