非线性多项式方程与相应雅可比矩阵之间的关系公式
Relationship formula between nonlinear polynomial equations and the corresponding Jacobian matrix
AI总结：
本文证明非线性多项式方程与雅可比矩阵间关系定理的普适性，并给出无需函数向量的牛顿公式及误差估计公式，拓展了非线性系统分析工具。
摘要：
本文为非线性模拟多项式方程与相应雅可比矩阵之间的关系定理提供了一个一般性证明，该定理最近由本文作者提出。该定理也被验证对所有非线性多项式代数方程组普遍有效。作为该定理的两个具体应用，我们给出了一个无需评估非线性函数向量的牛顿公式，以及一个用于估计近似雅可比矩阵相对误差的简单公式。最后，讨论了该定理在非线性系统分析中的一些可能应用。
英文摘要：
This paper provides a general proof of a relationship theorem between nonlinear analogue polynomial equations and the corresponding Jacobian matrix, presented recently by the present author. This theorem is also verified generally effective for all nonlinear polynomial algebraic system of equations. As two particular applications of this theorem, we gave a Newton formula without requiring the evaluation of nonlinear function vector as well as a simple formula to estimate the relative error of the approximate Jacobian matrix. Finally, some possible applications of this theorem in nonlinear system analysis are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
