Lagrange插值逼近导数的平均收敛  

MEAN CONVERGENCE OF DERIVATIVES BY LAGRANGE INTERPOLATION

作　　者：杜英芳[1] 许贵桥[1] 

机构地区：[1]天津师范大学化学与生命科学学院,天津300387

出　　处：《高等学校计算数学学报》2010年第1期47-55,共9页Numerical Mathematics A Journal of Chinese Universities

基　　金：support by National Natural Science Foundation of China(10471010);Education Science Foundation of Tianjin Normal University(52LJ80)

摘　　要：We consider the rate of mean convergence of derivatives by Lagrange interpolation operators L_n(f,x) based on the zeros of Chebyshev polynomials of the first kind.A sharp estimate of the derivative of L_n(f,x)—f(x) in terms of the error of best approximation by polynomials of degree n is derived.We consider the rate of mean convergence of derivatives by Lagrange interpolation operators Ln（f, x） based on the zeros of Chebyshev polynomials of the first kind. A sharp estimate of the derivative of Ln（f, x） -f（x） in terms of the error of best approximation by polynomials of degree n is derived.

关 键 词：Lagrange interpolation DERIVATIVE mean convergence best approximation 

分 类 号：O174.41[理学—数学]