论文标题
MACAULAY中的数字验证软件包2
The NumericalCertification package in Macaulay2
论文作者
论文摘要
软件包\ texttt {数值}实现了为给定的多项式方程系统确认解决方案的数值近似值的方法。为了证明常规解决方案，该软件包实施了Smale的$α$ - 理论和krawczyk方法。对于单数解决方案，我们使用迭代通缩方法实施软验证。我们演示了\ texttt {macaulay2}中与当前数值求解器交互的软件包的功能。
The package \texttt{NumericalCertification} implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regular solutions, the package implements Smale's $α$-theory and Krawczyk method. For a singular solution, we implement soft verification using the iterative deflation method. We demonstrate the functionalities of the package focusing on interaction with current numerical solvers in \texttt{Macaulay2}.
