scholarly journals Mean Convergence Rate of Derivatives by Lagrange Interpolation on Chebyshev Grids

2011 ◽  
Vol 2011 ◽  
pp. 1-22
Author(s):  
Wang Xiulian ◽  
Ning Jingrui
Keyword(s):  
Convergence Rate ◽  
Best Approximation ◽  
Lagrange Interpolation ◽  
Mean Convergence ◽  
Chebyshev Nodes ◽  
Approximation By Polynomials ◽  
Interpolation Operators

We consider the rate of mean convergence of derivatives by Lagrange interpolation operators based on the Chebyshev nodes. Some estimates of error of the derivatives approximation in terms of the error of best approximation by polynomials are derived. Our results are sharp.

Mean Convergence of Lagrange Interpolation for Exponential weights on [-1, 1]

1998 ◽  
Vol 50 (6) ◽  
pp. 1273-1297 ◽  
Author(s):  
D. S. Lubinsky
Keyword(s):  
Orthogonal Polynomials ◽  
Lagrange Interpolation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Exponential Weights ◽  
Mean Convergence ◽  
Zeros Of Orthogonal Polynomials ◽  
Necessary And Sufficient

AbstractWe obtain necessary and sufficient conditions for mean convergence of Lagrange interpolation at zeros of orthogonal polynomials for weights on [-1, 1], such asw(x) = exp(-(1 - x2)-α), α > 0orw(x) = exp(-expk(1 - x2)-α), k≥1, α > 0,where expk = exp(exp(. . . exp( ) . . .)) denotes the k-th iterated exponential.

scholarly journals A note on mean convergence of Lagrange interpolation in Lp(0

2001 ◽  
Vol 133 (1-2) ◽  
pp. 277-282 ◽  
Author(s):  
S.B. Damelin ◽  
H.S. Jung ◽  
K.H. Kwon
Keyword(s):  
Lagrange Interpolation ◽  
Mean Convergence
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