Expanding the applicability of the Secant method under weaker conditions

作者：

Highlights：

• Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved.

• Under the same computational cost on the parameters involved our convergence criteria are weaker than in earlier studies.

• Under the same computational cost on the parameters involved the error bounds are more precise than in earlier studies.

• Numerical examples are also presented to illustrate the theoretical results obtained in this study.

摘要

•Our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved.•Under the same computational cost on the parameters involved our convergence criteria are weaker than in earlier studies.•Under the same computational cost on the parameters involved the error bounds are more precise than in earlier studies.•Numerical examples are also presented to illustrate the theoretical results obtained in this study.

论文关键词：Secant method,Banach space,Majorizing sequence,Divided difference,Local convergence,Semilocal convergence

论文评审过程：Received 22 September 2014, Revised 29 May 2015, Accepted 9 June 2015, Available online 30 June 2015, Version of Record 30 June 2015.

论文官网地址：https://doi.org/10.1016/j.amc.2015.06.037