使用区间算术证明多项式系统的零点
Certifying zeros of polynomial systems using interval arithmetic
AI总结：
本研究将区间算术用于数值代数几何验证，在HomotopyContinuation.jl中实现基于Krawczyk方法的certify函数，可证明方形多项式方程组孤立非奇异解的正确性，性能远超现有方法，推动验证成为默认操作。
摘要：
我们将区间算术确立为数值代数几何中一种实用的验证工具。我们的软件HomotopyContinuation.jl现已内置certify（验证）函数，可证明方形多项式方程组孤立非奇异解的正确性。该实现基于Krawczyk方法。我们证明其性能显著优于以往的验证方法。我们认为这一成果是数值代数几何中强大的新工具，可使验证成为默认操作而非仅为可选功能。
英文摘要：
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.
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。
