An acceleration of the continuous Newton's method

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:354

Article; Proceedings Paper

Gutierrez, J. M.¹  Hernandez-Veron, M. A.¹ 

[1] Univ La Rioja, Dept Math & Comp Sci, Logrono, Spain

关键词: Continuous Newton's method;    Nonlinear equations;    Iterative methods;    Acceleration of convergence;   

DOI  :  10.1016/j.cam.2018.03.013

来源: Elsevier

【 摘 要 】

In this work, we study some numerical properties of the continuous Newton's method, the continuous version of the classical Newton's method for solving nonlinear equations p(z) = 0. In fact, continuous Newton's method is an initial value problem whose solutions flow to a root of the equation. We show the influence of the multiplicity of the roots of the considered equation in the Jacobian matrix related to the problem. In addition, we study some modifications of the continuous Newton's method that allow us to increase the velocity of the convergence of the solutions towards the roots of p(z) = 0. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free