A technique to choose the most efficient method between secant method and some variants

作者：Grau Sanchez Miquel^*; Noguera Miquel

来源：Applied Mathematics and Computation, 2012, 218(11): 6415-6426.

DOI：10.1016/j.amc.2011.12.011

• Divided difference
• Order of convergence
• Efficiency
• Nonlinear equations
• Iterative methods

A few variants of the secant method for solving nonlinear equations are analyzed and studied. In order to compute the local order of convergence of these iterative methods a development of the inverse operator of the first order divided differences of a function of several variables in two points is presented using a direct symbolic computation. The computational efficiency and the approximated computational order of convergence are introduced and computed choosing the most efficient method among the presented ones. Furthermore, we give a technique in order to estimate the computational cost of any iterative method, and this measure allows us to choose the most efficient among them.

• 出版日期2012-2-5