高阶可微函数的共单调逼近  

COMONOTONE APPROXIMATION OF HIGH DEGREE DIFFERENTIABLE FUNCTIONS

作　　者：孙德华[1] 刘三阳[1] 

机构地区：[1]西安电子科技大学理学院,西安710071

出　　处：《高等学校计算数学学报》2005年第S1期143-147,共5页Numerical Mathematics A Journal of Chinese Universities

摘　　要：1 引言设f(x)∈C[-1,1]是分段单调函数,若要求逼近f(x)的多项式pn(x)也是分段单调的,且在每一分段上,f(x)与pn(x)具有相同的单调性,则称这种形式的逼近为共单调逼近,记En(f)=inf{‖f(x)-pn(x)‖|pn(x)∈πn,pn(x)在[-1,1]上与f(x)共单调}。For the piecewise monotone functions, searching the polynomial which has the same character as monotone functions, is called comonotone approximation. The thought is of great importance in practice and theory of image proceeding, analysis of states and engineering computation, etc.. At present, there are many open problems though it has been developed more than 20 years. This paper discusses the comonotone approximation of a type of piecewise monotone function, by means of K-functional, etc., we obtain the ...

关 键 词：comonotone approximation K-FUNCTIONAL degree of approximation modulus of smoothness. 

分 类 号：O174[理学—数学]