ON THE GENERALIZATION OF SECANT METHOD AND THE ORDER OF CONVERGENCE

Vicente Candela; Natalia Expósito; Pedro J. Martínez−Aparicio; Juan Carlos Trillo

doi:10.11948/20240082

2025 Volume 15 Issue 1

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Vicente Candela, Natalia Expósito, Pedro J. Martínez−Aparicio, Juan Carlos Trillo. ON THE GENERALIZATION OF SECANT METHOD AND THE ORDER OF CONVERGENCE[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 245-260. doi: 10.11948/20240082

Citation:

Vicente Candela, Natalia Expósito, Pedro J. Martínez−Aparicio, Juan Carlos Trillo. ON THE GENERALIZATION OF SECANT METHOD AND THE ORDER OF CONVERGENCE[J]. Journal of Applied Analysis & Computation, 2025, 15(1): 245-260. doi: 10.11948/20240082

ON THE GENERALIZATION OF SECANT METHOD AND THE ORDER OF CONVERGENCE

1.
Departamento de Matemáticas, Universidad de Valencia, Spain
2.
Departamento de Matemáticas, Universidad de Almería, Spain
3.
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Spain

Author Bio: Email: vicente.candela@uv.es(V. Candela); Email: nes414@inlumine.ual.es(N. Expósito); Email: pedroj.ma@ual.es(P. J. Martínez−Aparicio); Email: jc.trillo@upct.es(J. C. Trillo)

Abstract

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.
- Nonlinear equations /
- Secant method /
- Müller method /
- order of convergence
MSC: 65H04, 65H05

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References

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