A Note on a Family of Newton Type Iterative Processes
نویسندگان
چکیده
In this paper, we study the convergence of a family of iteration methods to solve nonlinear equations in the complex plane. Two analysis of convergence are provided. We give a Kantorovich-type convergence theorem under mild differentiability conditions with error analysis.
منابع مشابه
A Composite Finite Difference Scheme for Subsonic Transonic Flows (RESEARCH NOTE).
This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...
متن کاملNumerical solution for the risk of transmission of some novel coronavirus (2019-nCov) models by the Newton-Taylor polynomial solutions
In this paper we consider two type of mathematical models for the novel coronavirus (2019-nCov), which are in the form of a nonlinear differential equations system. In the first model the contact rate, , and transition rate of symptomatic infected indeviduals to the quarantined infected class, , are constant. And in the second model these quantities are time dependent. These models are the...
متن کاملA Family of Newton Type Iterative Methods for Solving Nonlinear Equations
In this paper, a general family of n-point Newton type iterative methods for solving nonlinear equations is constructed by using direct Hermite interpolation. The order of convergence of the new n-point iterative methods without memory is 2 requiring the evaluations of n functions and one first-order derivative in per full iteration, which implies that this family is optimal according to Kung a...
متن کاملEvaluation of estimation methods for parameters of the probability functions in tree diameter distribution modeling
One of the most commonly used statistical models for characterizing the variations of tree diameter at breast height is Weibull distribution. The usual approach for estimating parameters of a statistical model is the maximum likelihood estimation (likelihood method). Usually, this works based on iterative algorithms such as Newton-Raphson. However, the efficiency of the likelihood method is not...
متن کاملHigh - order Newton - type iterative methods with memory for solving nonlinear equations ∗
In this paper, we present a new family of two-step Newton-type iterative methods with memory for solving nonlinear equations. In order to obtain a Newton-type method with memory, we first present an optimal two-parameter fourth-order Newton-type method without memory. Then, based on the two-parameter method without memory, we present a new two-parameter Newton-type method with memory. Using two...
متن کامل