Work

On the Generalization of Secant Method and the Order of Convergence

Year: 2025

Type: article

Abstract: In this paper we start generalizing the well known Secant and Müller methods by using higher degree polynomials. Although such generalization does already exist, we prove in an original and elegant way that the order of convergence $p$ is limited by p = 2. The techniques used in this paper could also be helpful in other contexts. We also perform some numerical experiments to reinforce the theoretical results.

Source: Journal of Applied Analysis & Computation

DOI: 10.11948/20240082

Authors: Vicente Candela, Natalia Expósito, Pedro J. Martínez−Aparicio, Juan Carlos Trillo

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4411533585

FWCI: 1.071

Cites:

Cited by: 1

Related to: 10