论文标题
零维多元真实非线性系统的认证数值真实根隔离
Certified Numerical Real Root Isolation of Zero-dimensional Multivariate Real Nonlinear Systems
论文作者
论文摘要
使用给定的零维平方多元非线性系统的局部几何特性，我们为盒子内部系统的独特性和实际简单零的唯一性和存在提供了一个简单但有效的新标准。基于结果，我们基于细分和间隔算术的算法设计算法，以隔离给定框中一般实际非线性系统的所有真实零。对于仅有有限隔离的简单真实零零的系统，我们的方法已完成。给出一般零维系统的终止精度。系统的多个零是在有限的框中输出的。各种基准显示了我们实施的有效性和效率（在C ++中）。它适用于Bezout绑定超过1亿个多项式系统。它还适用于非多功能非线性系统。我们还讨论了我们方法的局限性。
Using the local geometrical properties of a given zero-dimensional square multivariate nonlinear system inside a box, we provide a simple but effective and new criterion for the uniqueness and the existence of a real simple zero of the system inside the box. Based on the result, we design an algorithm based on subdivision and interval arithmetics to isolate all the real zeros of a general real nonlinear system inside a given box. Our method is complete for systems with only finite isolated simple real zeros inside a box. A termination precision is given for general zero-dimensional systems. Multiple zeros of the system are output in bounded boxes. A variety of benchmarks show the effectivity and efficiency of our implementation (in C++). It works for polynomial systems with Bezout bound more than 100 million. It also works for non-polynomial nonlinear systems. We also discuss the limitations of our method.
