An efficient method based on progressive interpolation for solving non-linear equations. (November 2016)

• Record Type: Journal Article
• Authors: Chen, Xiao-Diao; Zhang, Yubao; Shi, Jiaer; Wang, Yigang
• Is Part Of: Applied mathematics letters. Volume 61(2016:Nov.)
• Page Start: 67
• Page End: 72
• Publication Date: 2016-11
• Subjects: Root finding -- Progressive interpolation method -- Convergence rate -- Efficiency index -- Non-linear equations; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.05.007
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: 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.