A class of iterative methods with third-order convergence to solve nonlinear equations
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In this paper, the authors present a class of third-order iterative techniques in the form of x"k"+"1=g"u(x"k) =x k+f(x k)u (x k + u u(x)k) to solve a nonlinear equation f with the aid of a weight function u.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 2008-08-15 and is currently open access. It has received 9 citations till now. The article focuses on the topics: Function composition & Generic property.read more
Citations
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Journal ArticleDOI
Third-order iterative methods with applications to Hammerstein equations: A unified approach
TL;DR: The aim of the present paper is to analyze the convergence of this family for equations defined between two Banach spaces by using a technique developed in [J.A. Hernandez, Halley's method for operators with unbounded second derivative], and obtain a general semilocal convergence result for these methods.
Journal ArticleDOI
Simple geometry facilitates iterative solution of a nonlinear equation via a special transformation to accelerate convergence to third order
TL;DR: In this article, the authors study the convergence acceleration by generating secondary solvers through the transformation g"m"p"s(x)=x+g(x)-m(x)x)/(1-m(X)) or, equivalently, through partial substitution g" m"p's(X)=x +G(x)(g-x), G(x=1/(1-M(x)).
Journal Article
A Note on the “Constructing” of Nonstationary Methods for Solving Nonlinear Equations with Raised Speed of Convergence
Nikolay Kyurkchiev,Anton Iliev +1 more
TL;DR: In this article, a methodological survey of "contempo- rary methods" for solving the nonlinear equation f(x) = 0 is given, and one methodological schema for constructing nonstationary methods with a preliminary chosen speed of convergence is developed.
Journal ArticleDOI
A novel cubically convergent iterative method for computing complex roots of nonlinear equations
TL;DR: A fast and simple iterative method with cubic convergent that can find complex roots just by a real initial guess in contrast to many other methods like the famous Newton method that needs complex initial guesses for finding complex roots.
A Class of Iterative Methods of Third Order for Solving Nonlinear Equations
Fan Sha,Xueyuan Tan +1 more
TL;DR: For solving nonlinear equations, a novel class of iterative methods are proposed in this article, and convergence analysis shows that the proposed methods are cubic convergent and comparable to the well-known Newton method.
References
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Book
An introduction to numerical analysis
TL;DR: In this article, the authors present a solution to the Matrix Eigenvalue Problem for linear systems of linear equations, based on linear algebra and linear algebra with nonlinear functions, which they call linear algebraic integration.
Journal ArticleDOI
A variant of Newton's method with accelerated third-order convergence
TL;DR: It is shown that the order of convergence of the new method is three, and computed results support this theory.
Journal ArticleDOI
On Halley's Iteration Method
TL;DR: In this paper, Halley's Iteration Method is discussed and a discussion of the effect of the iterative method on the performance of the algorithm is presented. The American Mathematical Monthly: Vol. 92, No. 2, pp. 131-134.
Journal ArticleDOI
Accelerated convergence in Newton's method
TL;DR: Newton’s Method is based on a linear approximation of the function whose roots are to be determined taken at the current point, and the resulting algorithm is known to converge quadratically.
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