论文标题
使用间隔算术对多项式系统的零进行认证
Certifying zeros of polynomial systems using interval arithmetic
论文作者
论文摘要
我们建立间隔算术作为数值代数几何认证的实用工具。我们的软件shopopopyContination.jl现在具有内置函数认证，该功能证明了对多项式方程式方程式的隔离的非单位解决方案的正确性。该实现取决于Krawczyk的方法。我们证明，它极大地超过了早期的认证方法。我们将此贡献视为数值代数几何形状中强大的新工具，可以使认证成为默认值，而不仅仅是一个选项。
We establish interval arithmetic as a practical tool for certification in numerical algebraic geometry. Our software HomotopyContinuation.jl now has a built-in function certify, which proves the correctness of an isolated nonsingular solution to a square system of polynomial equations. The implementation rests on Krawczyk's method. We demonstrate that it dramatically outperforms earlier approaches to certification. We see this contribution as powerful new tool in numerical algebraic geometry, that can make certification the default and not just an option.
