Exact Formula for Solving a Degenerate System of Quadratic Equations
Pub Date : 2024-04-22
DOI:10.1134/s0965542524030072
引用次数: 0
Abstract
The paper is devoted to the solution of a nonlinear system of equations \(F(x{{) = 0}_{n}}\), where \(F\) is a quadratic mapping acting from \({{\mathbb{R}}^{n}}\) to \({{\mathbb{R}}^{n}}\). The derivative \(F{\kern 1pt} '\) is assumed to be degenerate at the solution point, which is a major characteristic property of nonlinearity of the mapping. Based on constructions of the p-regularity theory, a 2-factor method is proposed for solving the system of equations, which converges at a quadratic rate. Moreover, an exact formula is obtained for solving this quadratic system of equations in the case of a 2-regular mapping \(F(x)\).
求解一元二次方程系的精确公式
摘要 本文致力于非线性方程组 \(F(x{{) = 0}_{n}}\ 的求解，其中 \(F\) 是作用于 \({{\mathbb{R}}^{n}}\) 到 \({{\mathbb{R}}^{n}}\) 的二次映射。）假定导数 \(F{kern 1pt} '\) 在解点处是退化的，这是映射非线性的一个主要特征属性。基于 p-regularity 理论的构造，提出了一种求解方程组的 2 因子方法，该方法以二次方速率收敛。此外，在 2-regular 映射 \(F(x)\)的情况下，还得到了求解该二次方程组的精确公式。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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