A New Newton Method with Memory for Solving Nonlinear Equations

Xiaofeng Wang and Yuxi Tao
Additional contact information
Xiaofeng Wang: School of Mathematics and Physics, Bohai University, Jinzhou 121000, China
Yuxi Tao: School of Mathematics and Physics, Bohai University, Jinzhou 121000, China

Mathematics, 2020, vol. 8, issue 1, 1-9

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.

Keywords: simple roots; newton method; nonlinear equation; self-accelerating parameter; computational efficiency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/8/1/108/pdf (application/pdf)
https://www.mdpi.com/2227-7390/8/1/108/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:8:y:2020:i:1:p:108-:d:307186

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().