The W4 method: a new multi-dimensional root-finding scheme for nonlinear systems of equations
The W4 method: a new multi-dimensional root-finding scheme for nonlinear systems of equations
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DOI：
10.1016/j.apnum.2022.08.019
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发表时间：
2018-09
期刊：
影响因子：
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通讯作者：
Hirotada Okawa;K. Fujisawa;Yu Yamamoto;R. Hirai;N. Yasutake;H. Nagakura;S. Yamada
中科院分区：
文献类型：
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作者：
Hirotada Okawa;K. Fujisawa;Yu Yamamoto;R. Hirai;N. Yasutake;H. Nagakura;S. Yamada
我们提出了一类求解非线性方程组的新方法，除其他外，它具有四个优点：（i）它受到阻尼振子数学特性的启发，（ii）它可以被视为牛顿-拉夫森（NR）方法的简单扩展，（iii）它具有与 NR 方法相同的局部收敛性，（iv）它具有更宽的收敛区域或全局收敛性 与 NR 方法相比。在本文中，我们展示了这些属性的证据，将我们的新方法应用于一些示例，并将其与 NR 方法进行比较。
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.