The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the Chebyshev, the Halley and the super– Halley iterative methods. The goal is to show that if we are interesting to preserve the convergence properties we must ensure that the deriva...

the esophagogastric junction (gastric inlet obstruction; GIO) or antrum (gastric outlet obstruction; GOO) are unresectable and show local recurrence. Patients with GIO or GOO may present with swallowing difficulty or intractable vomiting, and/or the inability to eat, conditions which lead to a progressive deterioration in their quality of life. The consequences are weight loss and dehydration, ...

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.

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...

[1] A superposed epoch analysis of 100–300 substorms is performed to determine the median size and shape of the substorm-associated VLF chorus, magnetic bay, and Pi2 pulsation burst observed at the near-auroral Halley research station, Antarctica, and at the midlatitude Faraday station at three different local times (2230, 2330, 0130 MLT). The spatial and temporal properties of the magnetic bay...

Obesity is increasing at an alarming rate, and its related disorders are placing a considerable strain on our healthcare system. Although they are not always coincident, obesity is often accompanied by hyperlipidemia. Both obesity and hyperlipidemia are independently associated with atherosclerosis, nonalcoholic fatty liver disease (NAFLD), and insulin resistance (IR). Thus, we sought to determ...

We study the dynamics of a family of third-order iterative methods that are used to find roots of nonlinear equations applied to complex polynomials of degrees three and four. This family includes, as particular cases, the Chebyshev, the Halley and the super-Halley root-finding algorithms, as well as the so-called c-methods. The conjugacy classes of these iterative methods are found explicitly....

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...

Welcome to the first article in a new SIGMOD Record column: Distinguished Database Profiles, featuring interviews with pillars of the database community. I am not much of a traveler, but I plan to leave my nest in east central Illinois to bring you a new interview in each issue. In June I traveled to California to join in the festivities associated with Professor Gio Wiederhold’s retirement fro...