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6 results on '"Moysi, Alejandro"'

2. On the set of initial guesses for the secant method

Author

Moysi, Alejandro, Ezquerro, José Antonio, Hernández-Verón, Miguel Ángel, Magreñán, Ángel Alberto, 0000-0002-7138-4385, and 0000-0002-6991-5706

Subjects
Newton's method, General Mathematics, convergence ball, Hammerstein integral equation, General Engineering, local convergence, dynamics, the secant method, accessibility
Published
2023

5. Convergence and Dynamics of a Higher-Order Method

Author

Moysi, Alejandro, Argyros, Ioannis K., Regmi, Samundra, González, Daniel, Magreñán, A. Alberto, Sicilia, Juan Antonio, 0000-0002-7138-4385, 0000-0002-6991-5706, and 0000-0002-5962-4147

Subjects
Physics, Work (thermodynamics), Sequence, convergence, Physics and Astronomy (miscellaneous), Iterative method, General Mathematics, lcsh:Mathematics, Contrast (statistics), 010103 numerical & computational mathematics, Derivative, dynamics, lcsh:QA1-939, 01 natural sciences, 010101 applied mathematics, Nonlinear system, Chemistry (miscellaneous), Convergence (routing), Computer Science (miscellaneous), Order (group theory), Applied mathematics, high-order iterative method, 0101 mathematics
Abstract

Solving problems in various disciplines such as biology, chemistry, economics, medicine, physics, and engineering, to mention a few, reduces to solving an equation. Its solution is one of the greatest challenges. It involves some iterative method generating a sequence approximating the solution. That is why, in this work, we analyze the convergence in a local form for an iterative method with a high order to find the solution of a nonlinear equation. We extend the applicability of previous results using only the first derivative that actually appears in the method. This is in contrast to either works using a derivative higher than one, or ones not in this method. Moreover, we consider the dynamics of some members of the family in order to see the existing differences between them.

Published
2020

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