Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications

Amat, Sergio; Busquier, Sonia; Grau, íngela; Grau-Sánchez, Miquel

doi:10.1016/j.amc.2013.01.047

Cited by 27 publications

(27 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The maximum efficiency for a family of Newton-like methods with frozen derivatives, that is, the number k of sub-iterations, depends on the problem, but it can be computed before solving it. 13 Second family:…”

Section: Introductionmentioning

confidence: 99%

On two high‐order families of frozen Newton‐type methods

Amat

Argyros

Busquier

et al. 2017

Numerical Linear Algebra App

View full text Add to dashboard Cite

SummaryThis paper is devoted to the study of two high-order families of frozen Newton-type methods. The methods are free of bilinear operators, which constitute the main limitation of the classical high-order iterative schemes.Both families are natural generalizations of an efficient third-order method.Although the methods are more demanding, a semilocal convergence analysis is presented using weaker conditions.

show abstract

Section: Introductionmentioning

confidence: 99%

On two high‐order families of frozen Newton‐type methods

Amat

Argyros

Busquier

et al. 2017

Numerical Linear Algebra App

View full text Add to dashboard Cite

show abstract

“…In the multi-dimensional case CEI will be used to compare the efficiencies of different algorithms. Some significant discussions on the efficiency of iterative methods can also be found in [1,5,6,9,12,19].…”

Section: Clarification Of Main Conceptsmentioning

confidence: 99%

Note on the efficiency of some iterative methods for solving nonlinear equations

Sánchez

Batlle

Barrero

2015

SeMA

Self Cite

View full text Add to dashboard Cite

The efficiency of algorithms for solving nonlinear equations is a measure of comparison between different iterative methods. In the case of scalar equations two parameters are considered as it is well-known, but frequently in recent literature inaccurate generalizations combining these parameters are used when solving systems of nonlinear equations. Our goal in this paper is to clarify the concept of the efficiency in the multi-dimensional case. To do it we present a detailed definition of the computational efficiency. The relation between the efficiency parameters in scalar and vectorial cases is analyzed in detail and tested in two numerical examples.

show abstract

“…A thorough study of the cost and efficiency of iterative methods for nonlinear systems can be found in [5,10]. Nevertheless, we introduce a new term in the cost expression to take into account matrix-vector operations that occur in some iterative methods such as the considered here.…”

Section: Introductionmentioning

confidence: 99%

Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems

Hueso

Martínez

Teruel

2015

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

ElsevierMartínez Molada, E.; Hueso Pagoaga, JL.; Teruel, C. (2015). Convergence AbstractIn this work we present a new family of iterative methods for solving nonlinear systems that are optimal in the sense of Kung and Traub's conjecture for the unidimensional case. We generalize this family by performing a new step in the iterative method, getting a new family with order of convergence six. We study the efficiency of these families for the multidimensional case by introducing a new term in the computational cost defined by Grau-Sánchez et al. A comparison with already known methods is done by studying the dynamics of these methods in an example system.

show abstract

Maximum efficiency for a family of Newton-like methods with frozen derivatives and some applications

Cited by 27 publications

References 22 publications

On two high‐order families of frozen Newton‐type methods

On two high‐order families of frozen Newton‐type methods

Note on the efficiency of some iterative methods for solving nonlinear equations

Convergence, efficiency and dynamics of new fourth and sixth order families of iterative methods for nonlinear systems

Contact Info

Product

Resources

About