| Volume 15, Number 1, 2025, Pages - DOI：10.11948/JAAC-2024-0082 |
| On the generalization of secant method and the order of convergence |
| Juan Carlos Trillo,Vicente Candela,Natalia Expósito,Pedro J. Martínez-Aparicio |
| Keywords:Nonlinear equations, Secant Method, Muller method, order of convergence |
| Abstract: |
| In this paper we
start generalizing the well known Secant and M\text {\"u}ller 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. |
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