【摘要】 对高维单纯形上的Bernstein多项式进行了变形,通过减少多项式的项数以获得更好的计算效果,从而得到了两个修正Bernstein算子的模型,并且定义了新的函数类 文中利用函数构造法、不等式的缩放和单纯形上Bernstein算子的性质,研究了修正算子在一定条件下的收敛性和保证收敛的最小项数,同时给出了算子不收敛的范围更多还原

【Abstract】 Bernstein approximation is a kind of classic and abundant research subjects in the theory of approximations, which makes use of good properties and graceful structures of Bernstein polynomials to discuss a great deal of relations between Bernstein operators and the functions approached by it. In this paper, we transform the Bernstein polynomials on simplex of high dimension by decreasing the items of polynomials to get better calculation result. Two models of modified Bernstein operators are obtained and a new class of function is defined. By using the methods of function structure, the properties of inequality and Bernstein operators on simplex, the convergence of modified operators is investigated. An exact condition to insure the operators to converge with the smallest terms is also obtained.更多还原