TY - JOUR AU - Argyros, Ioannis K. AU - Magreñán, Alberto AU - Sarría, Íñigo AU - Sicilia, Juan Antonio PY - 2018 TI - Improved convergence analysis of the Secant method using restricted convergence domains with real-world applications JO - Journal of Nonlinear Sciences and Applications SP - 1215--1224 VL - 11 IS - 11 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.011.11.01 DO - 10.22436/jnsa.011.11.01 ID - Argyros2018 ER - TY - JOUR TI - On a higher order Secant method AU - S. Amat AU - S. Busquier JO - Appl. Math. Comput. PY - 2003 DA - 2003// VL - 141 ID - Amat2003 ER - TY - JOUR TI - Adaptive approximation of nonlinear operators AU - S. Amat AU - S. Busquier AU - M. Negra JO - Numer. Funct. Anal. Optim. PY - 2004 DA - 2004// VL - 25 ID - Amat2004 ER - TY - JOUR TI - Approximation of inverse operators by a new family of high-order iterative methods AU - S. Amat AU - J. A. Ezquerro AU - M. A. Hernández-Vern JO - Numer. Linear Algebra Appl. 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