The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations

Hirotada Okawa; Kotaro Fujisawa; Yu Yamamoto; Ryosuke Hirai; Nobutoshi Yasutake; Hiroki Nagakura; Shoichi Yamada

doi:10.1016/j.apnum.2022.08.019

The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations

Hirotada Okawa, Kotaro Fujisawa, Yu Yamamoto, Ryosuke Hirai, Nobutoshi Yasutake, Hiroki Nagakura, Shoichi Yamada

School of Physics and Astronomy

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

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 extension 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.

Original language	English
Pages (from-to)	157-172
Number of pages	16
Journal	Applied Numerical Mathematics
Volume	183
DOIs	https://doi.org/10.1016/j.apnum.2022.08.019
Publication status	Published - Jan 2023

Keywords

Iterative methods
Partial differential equations
System of nonlinear equations

Access to Document

10.1016/j.apnum.2022.08.019Licence: CC BY

Cite this

@article{8e0d9ebf0cd6479cab2fe884eb914ba4,

title = "The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations",

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 extension 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.",

keywords = "Iterative methods, Partial differential equations, System of nonlinear equations",

author = "Hirotada Okawa and Kotaro Fujisawa and Yu Yamamoto and Ryosuke Hirai and Nobutoshi Yasutake and Hiroki Nagakura and Shoichi Yamada",

note = "Funding Information: We would like to thank K.-i Maeda for helpful comments. We are grateful to Y. Eriguchi for valuable comments on the preliminary draft. H. O. is grateful to Z. Pelgrims for reproducing our result. This work was supported by JSPS KAKENHI Grant Number 16K17708 , 16H03986 , 17K18792 , 20K03953 , 20K14512 . R. H. was supported by JSPS overseas research fellowship No. 29-514 . K. F was supported by JSPS postdoctoral fellowships No. 16J10223 . H. N. was partially supported at Caltech through NSF award No. TCAN AST-1333520 and DOE SciDAC4 Grant DE-SC0018297 (subaward 00009650). S. Y. is supported by the Institute for Advanced Theoretical and Experimental Physics , Waseda University and the Waseda University Grant for Special Research Projects (project number: 2020C-273 , 2021C-197 , 2022C-140 ). Publisher Copyright: {\textcopyright} 2022 The Authors",

year = "2023",

month = jan,

doi = "10.1016/j.apnum.2022.08.019",

language = "English",

volume = "183",

pages = "157--172",

journal = "Applied Numerical Mathematics",

issn = "0168-9274",

publisher = "Kluwer Academic Publishers",

}

TY - JOUR

T1 - The W4 method

T2 - A new multi-dimensional root-finding scheme for nonlinear systems of equations

AU - Okawa, Hirotada

AU - Fujisawa, Kotaro

AU - Yamamoto, Yu

AU - Hirai, Ryosuke

AU - Yasutake, Nobutoshi

AU - Nagakura, Hiroki

AU - Yamada, Shoichi

N1 - Funding Information: We would like to thank K.-i Maeda for helpful comments. We are grateful to Y. Eriguchi for valuable comments on the preliminary draft. H. O. is grateful to Z. Pelgrims for reproducing our result. This work was supported by JSPS KAKENHI Grant Number 16K17708 , 16H03986 , 17K18792 , 20K03953 , 20K14512 . R. H. was supported by JSPS overseas research fellowship No. 29-514 . K. F was supported by JSPS postdoctoral fellowships No. 16J10223 . H. N. was partially supported at Caltech through NSF award No. TCAN AST-1333520 and DOE SciDAC4 Grant DE-SC0018297 (subaward 00009650). S. Y. is supported by the Institute for Advanced Theoretical and Experimental Physics , Waseda University and the Waseda University Grant for Special Research Projects (project number: 2020C-273 , 2021C-197 , 2022C-140 ). Publisher Copyright: © 2022 The Authors

PY - 2023/1

Y1 - 2023/1

N2 - 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 extension 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.

AB - 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 extension 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.

KW - Iterative methods

KW - Partial differential equations

KW - System of nonlinear equations

UR - http://www.scopus.com/inward/record.url?scp=85138101476&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2022.08.019

DO - 10.1016/j.apnum.2022.08.019

M3 - Article

AN - SCOPUS:85138101476

SN - 0168-9274

VL - 183

SP - 157

EP - 172

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

ER -

The W4 method: A new multi-dimensional root-finding scheme for nonlinear systems of equations

Abstract

Keywords

Access to Document

Other files and links

ARC Centre of Excellence for Gravitational Wave Discovery

Cite this