Another Newton-type method with (k+2) order convergence for solving quadratic equations
Journal Title: JOURNAL OF ADVANCES IN MATHEMATICS - Year 2016, Vol 12, Issue 9
Abstract
In this paper we define another Newton-type method for finding simple root of quadratic equations. It is proved that the new one-point method has the convergence order of k  2 requiring only three function evaluations per full iteration,where k is the number of terms in the generating series. The Kung and Traub conjecture states that the multipoint iteration methods, without memory based on n function evaluations, could achieve maximum convergence order 1 2nï€ but, the new method produces convergence order of nine, which is better than the expected maximum convergence order. Finally, we have demonstrated that our present method is very competitive with the similar methods.
Authors and Affiliations
R Thukral
Keywords
Related Articles
- EP ID EP651687
- DOI 10.24297/jam.v12i9.128
- Views 200
- Downloads 0
Approximation to the Mean and Variance of the Modified Moments Estimator of the Shape Parameter of Weibull Distribution
In this paper we consider the Weibull distribution of two parameters , since has been widely used as a model in many areas of applications. Properties of the distribution are introduced . Estimation of the distribution p...
Nonlinear Fredholm-Volterra Integral Equation and its Numerical Solutions with Quadrature Methods
In this work, the existence and uniqueness of solution of the nonlinear Fredholm-Volterra integral equation (NF-VIE), with continuous kernels, are discussed and proved in the space L2(Ω)—C(0,T). The Fredholm integ...
FERMAT'S LAST THEOREM: ALGEBRAIC PROOF
In 1995, A, Wiles announced, using cyclic groups, a proof of Fermat's Last Theorem, which is stated as follows: If is an odd prime and x; y; z are relatively prime positive integers, then . In this note, a proof of...
A NOTE ON PARTIALLY ORDERED FUZZY METRIC SPACE VIA COUPLED COINCIDENCE POINTS
In this paper, we prove a coupled coincidence point theorem in partially ordered fuzzy metric space using Ï•-contractive condition.
A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition
In this paper, we shall discuss the uniqueness ”pathwise uniqueness” of the solutions of stochastic partial differential equations (SPDEs) with non-local initial condition,We shall use the Yamada-Watanabe condi...