The W4 method: a new multi-dimensional root-finding scheme for nonlinear systems of equations
Numerical Analysis
2018-09-13 v1 Instrumentation and Methods for Astrophysics
General Relativity and Quantum Cosmology
Numerical Analysis
Chaotic Dynamics
Abstract
We propose a new class of method for solving nonlinear systems of equations, which, among other things,has four nice features: (i) it is inspired by the mathematical property of damped oscillators, (ii) it can be regarded as a simple extention to the Newton-Raphson(NR) method, (iii) it has the same local convergence as the NR method does, (iv) it has a significantly wider convergence region or the global convergence than that of the NR method. In this article, we present the evidence of these properties, applying our new method to some examples and comparing it with the NR method.
Cite
@article{arxiv.1809.04495,
title = {The W4 method: a new multi-dimensional root-finding scheme for nonlinear systems of equations},
author = {Hirotada Okawa and Kotaro Fujisawa and Yu Yamamoto and Ryosuke Hirai and Nobutoshi Yasutake and Hiroki Nagakura and Shoichi Yamada},
journal= {arXiv preprint arXiv:1809.04495},
year = {2018}
}
Comments
17 pages, 7 figures