Extending the convergence domain of the Secant and Moser method in Banach Space

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:290

Article

Argyros, Ioannis K.¹  Alberto Magrenan, A.² 

[1] Cameron Univ, Dept Math Sci, Lawton, OK 73505 USA

[2] Univ Int La Rioja, Escuela Ingn, Logrono 26002, Spain

关键词: Newton's method;    Secant method;    Moser method;    Semilocal convergence;    Recurrent relations;    Banach space;   

DOI  :  10.1016/j.cam.2015.05.005

来源: Elsevier

【 摘 要 】

We present a new semilocal convergence analysis for the Secant and the Moser method in order to approximate a solution of an equation in a Banach space setting. Using the method of recurrent relations and weaker sufficient convergence criteria than in earlier studies such as Amat et al. (2014), Hernandez and Rubio (2007), Hernandez and Rubio (1999) and Hernandez and Rubio (2002) we increase the convergence domain of these methods. The advantages are also obtained under less computational cost than in Amat et al. (2014), Hernandez and Rubio (2007), Hernandez and Rubio (1999) and Hernandez and Rubio (2002). Numerical examples where the older convergence criteria are not satisfied but the new convergence criteria are satisfied are also provided in this study. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free