Journal ArticleDOI
On a family of multipoint methods for non-linear equations
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In this paper, a new one-parameter family of methods for finding simple zeros of non-linear functions is developed, each member of the family requires four evaluations of the given function and only one evaluation of the derivative per step.Abstract:
A new one-parameter family of methods for finding simple zeros of non-linear functions is developed. Each member of the family requires four evaluations of the given function and only one evaluation of the derivative per step. The order of the method is 16.read more
Citations
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Journal ArticleDOI
Basin attractors for various methods
TL;DR: It can be seen that not all higher order methods were created equal, namely the basin of attraction of the method and its dependence on the order.
Journal ArticleDOI
A family of modified Ostrowski methods with accelerated sixth order convergence
Janak Raj Sharma,Rangan K. Guha +1 more
TL;DR: A one-parameter family of sixth order methods for solving equations that requires three evaluations of the given function and one evaluation of its derivative per iteration is derived.
Journal ArticleDOI
Multipoint methods for solving nonlinear equations: A survey
TL;DR: This survey paper is intended as a review of the most efficient root-finding algorithms and developing techniques in a general sense and special attention is devoted to multipoint methods with memory that use already computed information to considerably increase convergence rate without additional computational costs.
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Basins of attraction for optimal eighth order methods to find simple roots of nonlinear equations
TL;DR: It is discovered that the eighth order methods based on Jarratt's optimal fourth order methods perform well and those based on King's or Kung-Traub's methods do not.
Journal ArticleDOI
Families of optimal multipoint methods for solving nonlinear equations: A survey
TL;DR: In this article, a review of optimal multipoint methods of the order four (n = 2), eight (n= 3), and higher (n > 3) is presented.
References
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Book
Iterative Methods for the Solution of Equations
TL;DR: One-point iteration functions with memory have been studied extensively in the literature as discussed by the authors, where it is shown that one-point iterators with memory achieve linear and superlinear convergence with respect to a fixed-point problem.
Journal ArticleDOI
Elementary numerical analysis: an algorithmic approach (2nd edition), by S. D. Conte and Carl de Boor. Pp x, 396. £4·80 hard covers, £2·70 paperback. 1973 (McGraw-Hill)
TL;DR: Intended for introductory courses in numerical analysis, this book features a comprehensive treatment of major topics in this subject area using an algorithmic approach and provides numerous worked examples with computer output, and flowcharts and programs.
Book
Elementary Numerical Analysis: An Algorithmic Approach
Samuel Daniel Conte,Carl de Boor +1 more
TL;DR: In this article, a comprehensive treatment of major topics in numerical analysis is presented, using an algorithmic approach, providing numerous worked examples with computer output, and flowcharts and programs.