On the Study of Highly Reliable Symbolic-Numeric Computation for Algebraic Problems with Empirical Data

我们提出了具有经验数据的代数问题的高可靠的符号-数值计算方法。主要结果如下。(1)多项式可整除性的确定算法。(2)稳定技术的新应用。(3)多项式系统解保持性质的极大摄动计算算法。此外，我们分析了计算时间，以找到在给定复域中具有零且最接近给定实单变量多项式的实单变量多项式。

We proposed highly reliable symbolic-numeric computation methods for algebraic problems with empirical data. Some main results are as follows.(1) An algorithm to determine divisibility of polynomials.(2) A new application of stabilization techniques.(3) An algorithm to compute the maximal perturbations for preserving properties of solutions of a polynomial system. Furthermore, we analyzed computing time to find a real univariate polynomial that has a zero in a given complex domain and is nearest to a given real univariate polynomial.