多项式根处Hölder连续函数的证明求值
Certified evaluations of Hölder continuous functions at roots of polynomials
摘要：
各种方法可以获得多项式根的认证估计。在科学和工程中的许多应用程序还利用在根处评估的函数的值。例如，通过在临界点处评估目标函数来获得临界值。对于解析评价函数，牛顿方法自然适用于产生经证明的估计。然而，这些估计不再适用于Hölder连续函数，这是Lipschitz连续函数的推广，其中连续导数不需要存在。这项工作开发和分析了一种替代方法，用于评估多项式根处的局部Hölder连续函数的认证估计。该方法在Maple中的实现证明了其有效性和效率。
英文摘要：
Various methods can obtain certified estimates for roots of polynomials. Many applications in science and engineering additionally utilize the value of functions evaluated at roots. For example, critical values are obtained by evaluating an objective function at critical points. For analytic evaluation functions, Newton's method naturally applies to yield certified estimates. These estimates no longer apply, however, for Hölder continuous functions, which are a generalization of Lipschitz continuous functions where continuous derivatives need not exist. This work develops and analyzes an alternative approach for certified estimates of evaluating locally Hölder continuous functions at roots of polynomials. An implementation of the method in Maple demonstrates efficacy and efficiency.
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