摘要
规划搜索是从初始状态S。经过中间目标S_1,S_2……,S_1达到目标状态S_9=S_(f+1)的搜索方法,用于求n次代数方程的实根时S_0是根模上,下界所划的区间,S_0是宽度小于允许误差的有根区间。这样的有根区间上、下限的平均值是根的较准确的近似值。为了使搜索方法可靠,在预处理中用Sturm定理判断实根个数和正、负根的个数,当搜索出的根少于判断个数时将测点加密重新搜索。引入求根辅助函数g(x)=f(x)/f_m(x),f_m(x)是sturm序列最后非零函数。在f(x)=(x-α)~n时g(x)=x-α。这就园满解决了含重根的病态方程的求根问题。
Plan search is a search method from initial state s_0 through middle states S_1, S_2,……S_1 to goal sfafe S_0=S_(1+1). Using this search method to finding real roots of n degree algebraic equations, So is the interva decided by upper modulus and lower modulus of the roots. There is a So on each side of original coordinate. Sg is a rooted interval whose width is smaller than the allowed error, the mean of upper limit and lower limit of it is the more accurate approximation of the root.
For the sake of reliable of the search method, determine the number of real roots, positive roots and negative roots with the aid of Sturm's the orem in preproeessing. When the number of searched roots less than the number of determined,increase the test points and search again. Introdueean auxiliary finding roots function of f(x): g(x)=f(x)/f_m(x).
This f_m(x) is the last nonzero function of sturm sequence。when f(x)= (x-2)~m, g(x)=x-2, so the problem of finding roots of the multiple roots algebraic equations is solved satisfactorily and the accuracy of the approximation of roots of ill algebraic equationscontained multiple roots is increased.
关键词
规划搜索
代数方程求根
plan search
finding roots of algebraic equations
