平方多项式-指数方程组解的认证
Certifying solutions to square systems of polynomial-exponential equations
AI总结：
本文基于Smale的alpha理论，通过推导相关多项式-指数方程组的高阶导数界，提出并实现了平方多项式-指数方程组解的完整认证算法。
摘要：
Smale的alpha理论基于给定点的牛顿残差和所有高阶导数，证明牛顿迭代将二次收敛到解析函数平方系统的一个解。Shub和Smale给出了多项式方程组高阶导数的一个界，该界部分基于方程的次数。对于给定的多项式-指数方程组，我们考虑一个相关的多项式-指数方程组，并给出了该相关方程组高阶导数的界。这个界产生了一个完整的算法，用于认证多项式-指数系统的解，该算法已在alphaCertified中实现。给出了示例来演示这个认证算法。
英文摘要：
Smale's alpha-theory certifies that Newton iterations will converge quadratically to a solution of a square system of analytic functions based on the Newton residual and all higher order derivatives at the given point. Shub and Smale presented a bound for the higher order derivatives of a system of polynomial equations based in part on the degrees of the equations. For a given system of polynomial-exponential equations, we consider a related system of polynomial-exponential equations and provide a bound on the higher order derivatives of this related system. This bound yields a complete algorithm for certifying solutions to polynomial-exponential systems, which is implemented in alphaCertified. Examples are presented to demonstrate this certification algorithm.
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。
