A fast and robust method for computing real roots of nonlinear equations. (June 2017)

• Record Type: Journal Article
• Authors: Chen, Xiao-Diao; Shi, Jiaer; Ma, Weiyin
• Is Part Of: Applied mathematics letters. Volume 68(2017:Jun.)
• Page Start: 27
• Page End: 32
• Publication Date: 2017-06
• Subjects: Root finding -- Non-linear equations -- Linear equations -- Progressive formula -- Optimal convergence order; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2016.12.013
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: The root-finding problem of a univariate nonlinear equation is a fundamental and long-studied problem, and has wide applications in mathematics and engineering computation. This paper presents a fast and robust method for computing the simple root of a nonlinear equation within an interval. It turns the root-finding problem of a nonlinear equation into the solution of a set of linear equations, and explicit formulae are also provided to obtain the solution in a progressive manner. The method avoids the computation of derivatives, and achieves the convergence order 2 n − 1 by using n evaluations of the function, which is optimal according to Kung and Traub's conjecture. Comparing with the prevailing Newton's methods, it can ensure the convergence to the simple root within the given interval. Numerical examples show that the performance of the derived method is better than those of the prevailing methods.