Improved convergence analysis of the Secant method using restricted convergence domains with real-world applications
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Authors
Ioannis K. Argyros
- Department of Mathematics Sciences, Cameron University, Lawton, OK 73505, USA.
Alberto Magreñán
- Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Av de la Paz, 137, 26002 Logroño, La Rioja, Spain.
Íñigo Sarría
- Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Av de la Paz, 137, 26002 Logroño, La Rioja, Spain.
Juan Antonio Sicilia
- Escuela Superior de Ingeniería y Tecnología, Universidad Internacional de La Rioja, Av de la Paz, 137, 26002 Logroño, Spain, Av de la Paz, 137, 26002 Logroño, La Rioja, Spain.
Abstract
In this paper, we are concerned with the problem of approximating a solution of a nonlinear equations by means of using the Secant method. We present a new semilocal convergence analysis for Secant method using restricted convergence domains. According to this idea we find a more precise domain where the inverses of the operators involved exist than in earlier studies. This way we obtain smaller Lipschitz constants leading to more precise majorizing sequences. Our convergence criteria are weaker and the error bounds are more precise than in earlier studies. Under the same computational cost on the parameters involved our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Different real-world applications are also presented to illustrate the theoretical results obtained in this study.
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ISRP Style
Ioannis K. Argyros, Alberto Magreñán, Íñigo Sarría, Juan Antonio Sicilia, Improved convergence analysis of the Secant method using restricted convergence domains with real-world applications, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 11, 1215--1224
AMA Style
Argyros Ioannis K., Magreñán Alberto, Sarría Íñigo, Sicilia Juan Antonio, Improved convergence analysis of the Secant method using restricted convergence domains with real-world applications. J. Nonlinear Sci. Appl. (2018); 11(11):1215--1224
Chicago/Turabian Style
Argyros, Ioannis K., Magreñán, Alberto, Sarría, Íñigo, Sicilia, Juan Antonio. "Improved convergence analysis of the Secant method using restricted convergence domains with real-world applications." Journal of Nonlinear Sciences and Applications, 11, no. 11 (2018): 1215--1224
Keywords
- Secant method
- Banach space
- majorizing sequence
- divided difference
- local convergence
- semilocal convergence
MSC
- 65H10
- 65G99
- 65B05
- 65N30
- 47H17
- 49M15
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