In a recent paper, Noor and Noor [K. Inayat Noor, M. Aslam Noor, Predictor–corrector Halley method for nonlinear equations, Appl. Math. Comput., in press, doi:10.1016/j.amc.11.023] have suggested and analyzed a predictor–corrector method Halley method for solving nonlinear equations. In this paper, we modified this method by using the finite difference scheme, which has a quintic convergence. W...

In the present work, the non-spherical grain characteristics of comet Halley are analysed using the T-matrix method at λ= 0.365,0.485 and 0.684μm respectively. In order to analyse the polarisation data of comet Halley, the dust size distribution function derived by Das et al. (2004) for comet Halley is used in the present work. The size range of the grains is taken to be 0.01μm≤ s ≤ 3μm. Using ...

Halley’s method is a famous iteration method for solving nonlinear equations F (X) = 0. Some Kantorovich-like theorems have been given, including extensions for general spaces. Quasi-Halley methods were proposed too. This paper uses the generalized inverse approach in order to obtain a robust generalized Halley method.

‎in this paper‎, ‎we present a new modification of chebyshev-halley‎ ‎method‎, ‎free from second derivatives‎, ‎to solve nonlinear equations‎. ‎the convergence analysis shows that our modification is third-order‎ ‎convergent‎. ‎every iteration of this method requires one function and‎ ‎two first derivative evaluations‎. ‎so‎, ‎its efficiency index is‎ ‎$3^{1/3}=1.442$ that is better than that o...

For each natural number m ≥ 3, we give a rootfinding method Hm, with cubic order of convergence for simple roots. However, for quadratic polynomials the order of convergence of Hm is m. Each Hm depends on the input, the corresponding function value, as well as the first two derivatives. We shall refer to this family as Halley Family, since H3 is the well-known method of Halley. For all m ≥ 4, t...

Keywords: Basin of attraction Simple roots Nonlinear equations Halley method Euler–Chebyshev method a b s t r a c t There are many methods for solving a nonlinear algebraic equation. Here we introduce a family of Halley-like methods and show that Euler–Chebyshev and BSC are just members of the family. We discuss the conjugacy maps and the effect of the extraneous roots on the basins of attracti...

In this paper, we suggest and analyze a new two-step predictor–corrector type iterative methods for solving nonlinear equations of the type f(x) = 0 by using the technique of updating the solution. This method can be viewed as a predictor– corrector iterative Halley’s method. We also consider the convergence analysis of the proposed method. To illustrate the efficiency of this new method, we gi...

We introduce a dynamically weighted Halley (DWH) iteration for computing the polar decomposition of a matrix, and prove that the new method is globally and asymptotically cubically convergent. For matrices with condition number no greater than 1016, the DWH method needs at most 6 iterations for convergence with the tolerance 10−16. The Halley iteration can be implemented via QR decompositions w...