An efficient method based on progressive interpolation for solving non-linear equations

作者：Chen, Xiao-Diao; Zhang, Yubao; Shi, Jiaer; Wang, Yigang^*

来源：Applied Mathematics Letters, 2016, 61: 67-72.

DOI：10.1016/j.aml.2016.05.007

• Root finding
• Progressive interpolation method
• Convergence rate
• Efficiency index
• Non-linear equations

The root-finding problem of a univariate polynomial is a fundamental and long studied problem, which has wide applications in mathematics, engineering, computer science, and natural sciences. This paper presents a progressive interpolation based method for solving a simple root within a given interval, which is of convergence order 3.2(n-3) and needs n functional evaluations of the given function f(t). The new method can ensure the convergence and achieve a better efficiency index. It needs none of the evaluations of the derivatives of f (t). Numerical examples show the convergence order of the progressive method.

• 出版日期2016-11
• 单位杭州电子科技大学