基于混合计算的非线性代数方程组的实根求解  

Finding Real Solutions of Nonlinear Algebraic Equations Based on Symbolic-Numeric Methods

作　　者：张瑾[1] 李耀辉[2] 

机构地区：[1]华北科技学院计算机科学与技术系,北京101601 [2]天津工程师范学院计算机科学与技术系,天津300222

出　　处：《江南大学学报（自然科学版）》2007年第2期144-149,共6页Joural of Jiangnan University (Natural Science Edition)　

基　　金：国家973计划项目(NKBRSF-2004CB318003)

摘　　要：利用Grbner基理论将多项式方程组的求解化为有限维代数问题,并进一步化为单变元方程w(xi)的求根,然后利用区间方法求出每个单变元方程的根区间,最后使用区间分析从变元根区间的全排列中找出方程组的区间解.在区间分析求解中,提出并证明了区间解的性质定理,该方法易于并行化,不产生误差积累,且可以找到全部方程组的实解并达到任意精度.By using Groebner basis, the paper transforms the multivariate nonlinear equations PS into univariate one ω（xi） over finite algebra. Then, the paper uses interval method to implement real root isolation for each ω（xi）. Finally, these real roots in different variants are combined to take as the possible solution of PS. We find the true solutions of PS from these combination by using interval analysis. In the paper, the theorem about properties of interval solution of PS is proposed and proved. The-advantage of our method is no error accumulation and easy to be parallelized. Besides these, it can find all real solutions with arbitrary precision for nonlinear algebraic equations.

关 键 词：混合计算 GROEBNER基 特征值 区间分析 实根求解 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构] O151[自动化与计算机技术—计算机科学与技术]