Abstract
A new Newton method with memory is proposed by using a variable self-accelerating parameter. Firstly, a modified Newton method without memory with invariant parameter is constructed for solving nonlinear equations. Substituting the invariant parameter of Newton method without memory by a variable self-accelerating parameter, we obtain a novel Newton method with memory. The convergence order of the new Newton method with memory is 1 + 2 . The acceleration of the convergence rate is attained without any additional function evaluations. The main innovation is that the self-accelerating parameter is constructed by a simple way. Numerical experiments show the presented method has faster convergence speed than existing methods.
Highlights
Using information from the current and previous iterations, iterative methods with memory for solving nonlinear equations can attain high convergence order and computational efficiency without any additional function evaluations
The main innovation is that the self-accelerating parameter is constructed by a simple way
The major innovative work of this paper is that we present a novel way to construct the self-accelerating parameter
Summary
Using information from the current and previous iterations, iterative methods with memory for solving nonlinear equations can attain high convergence order and computational efficiency without any additional function evaluations. √ [1] first proposed the following iterative method with memory with the convergence order 1 + 2 ≈ 2.414. The self-accelerating parameters usually are constructed by the interpolation method. A new way to construct the self-accelerating parameter is proposed and a simple modified Newton method with memory is obtained. The major innovative work of this paper is that we present a novel way to construct the self-accelerating parameter. The order of convergence of new method with memory is increased from 2 to 1 + 2 without any additional functional evaluations. Numerical experiments show that the new method has faster convergence speed than the existing methods
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
