Author(s): Cao Meng
Pages: 649-660
Year: 2014 Issue:  6
Journal: Pure and Applied Mathematics
Keyword:  Bernstein polynomial; classical Bezoutian matrix; Bernstein Bezoutian matrix; algorithm; uniform approximation form;
Abstract: 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.