Bezoutian矩阵的一致逼近形式

借助闭区间上的连续函数可以用Bernstein 多项式一致逼近这一事实,将多项式对所生成的经典Bezoutian 矩阵和Bernstein Bezoutian 矩阵推广到C [0,1]上函数对所对应的情形,给出了 Bezoutian 矩阵一致逼近形式的定义,并且得到如下结论：给出了经典 Bezoutian 矩阵的 Barnett 型分解公式和三角分解公式的一致逼近形式；提供了经典Bezoutian 矩阵和Bernstein Bezoutian 矩阵的一致逼近形式的两类算法；得到了上述两种矩阵的一致逼近形式中元素间的两个恒等关系式。最后,利用数值实例对恒等关系式进行验证,结果表明两类算法是有效的。

The uniform approximation form of Bezoutian matrix

Using the fact that Bernstein polynomial has the character of uniform approximation to continuous function on a closed interval, we generalize the classical Bezoutian matrix and Bernstein Bezoutian matrix gen-erated by a pair of polynomials to functions on the closed interval. The definition on the uniform approximation of Bezoutian matrices is given. And we obtain some conclusions about them. Firstly the uniform approximation form of the Barnett type factorization and triangular factorization formulas of classical Bezoutian matrix are presented. Secondly the algorithms of the uniform approximation form with respect to the classical Bezoutian matrix and Bernstein Bezoutian matrix are provided. Furthermore, we obtain two identical relations on ele-ments of the uniform approximation form relative to the two matrices mentioned before. Finally the numerical example is presented to verify the identical relation and show the effectiveness of the algorithms.