کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4608710 1338374 2013 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the Secant method
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
On the Secant method
چکیده انگلیسی

We present a new semilocal convergence analysis for the Secant method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our analysis is based on the weaker center-Lipschitz concept instead of the stronger Lipschitz condition which has been ubiquitously employed in other studies such as Amat et al. (2004)  [2], Bosarge and Falb (1969)  [9], Dennis (1971)  [10], Ezquerro et al. (2010)  [11], Hernández et al. (2005, 2000)  [13] and [12], Kantorovich and Akilov (1982)  [14], Laasonen (1969)  [15], Ortega and Rheinboldt (1970)  [16], Parida and Gupta (2007)  [17], Potra (1982, 1984–1985, 1985)  [18], [19] and [20], Proinov (2009, 2010)  [21] and [22], Schmidt (1978) [23], Wolfe (1978)  [24] and Yamamoto (1987)  [25] for computing the inverses of the linear operators. We also provide lower and upper bounds on the limit point of the majorizing sequences for the Secant method. Under the same computational cost, our error analysis is tighter than that proposed in earlier studies. Numerical examples illustrating the theoretical results are also given in this study.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Complexity - Volume 29, Issue 6, December 2013, Pages 454–471
نویسندگان
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