A class of modified Secant methods for unconstrained optimization

作者：Ren Hongmin^*; Wu Qingbiao

来源：Applied Mathematics and Computation, 2008, 206(2): 716-720.

DOI：10.1016/j.amc.2008.09.008

• Unconstrained optimization
• Iterative method
• Modified Secant method
• Wang's method
• Quadratical convergence

A class of modified Secant methods for solving univariate and unconstrained optimization problems is presented. The class takes the classical Secant method and a new variant of the Secant method proposed in Kahya and Chen [E. Kahya, J. H. Chen, A modified Secant method for unconstrained optimization, Appl. Math. Comput. 186 (2007) 1000-1004] as its special cases. This class also includes Wang's method with quadratical convergence proposed in Wang [X. H. Wang, Convergence iteration method of order two for finding zeros of the derivative, Math. Numer. Sinica 3 (1979) 209-220 (in Chinese)]. A unified convergence analysis as well as numerical examples show that Wang's method is the best one among all members of the class.

• 出版日期2008-12-15
• 单位浙江大学