scholarly journals Bivariate Lagrange interpolation at the Chebyshev nodes

2010 ◽  
Vol 138 (12) ◽  
pp. 4447-4447 ◽  
Author(s):  
Lawrence A. Harris
Keyword(s):  
Lagrange Interpolation ◽  
Chebyshev Nodes

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.

scholarly journals An extension of the Grünwald–Marcinkiewicz interpolation theorem

2001 ◽  
Vol 63 (2) ◽  
pp. 299-320 ◽  
Author(s):  
T. M. Mills ◽  
P. Vértesi
Keyword(s):  
Lagrange Interpolation ◽  
Interpolation Theorem ◽  
Higher Order ◽  
Classical Theorem ◽  
Chebyshev Nodes ◽  
Lagrange Interpolation Polynomials ◽  
Marcinkiewicz Interpolation Theorem ◽  
Interpolation Polynomials ◽  
Special Case

Just over 60 years ago, G. Grünwald and J. Marcinkiewicz discovered a divergence phenomenon pertaining to Lagrange interpolation polynomials based on the Chebyshev nodes of the first kind. The main result of the present paper is an extension of their now classical theorem. In particular, we shall show that this divergence phenomenon occurs for odd higher order Hermite–Fejér interpolation polynomials of which Lagrange interpolation polynomials form one special case.

scholarly journals On Hermite-Fejér type interpolation on the Chebyshev nodes

1993 ◽  
Vol 47 (1) ◽  
pp. 13-24 ◽  
Author(s):  
Graeme J. Byrne ◽  
T.M. Mills ◽  
Simon J. Smith
Keyword(s):  
Approximation Error ◽  
Interpolation Polynomial ◽  
Precise Estimate ◽  
Type Interpolation ◽  
Interpolation Methods ◽  
Chebyshev Nodes ◽  
Interpolatory Process

Given f ∈ C [−1, 1], let Hn, 3(f, x) denote the (0,1,2) Hermite-Fejér interpolation polynomial of f based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |Hn, 3(f, x) − f(x)|. Further, we demonstrate a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the Chebyshev nodes to obtain a convergent rational interpolatory process.

scholarly journals Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves

2015 ◽  
Vol 133 (4) ◽  
pp. 685-705 ◽  
Author(s):  
Wolfgang Erb ◽  
Christian Kaethner ◽  
Mandy Ahlborg ◽  
Thorsten M. Buzug
Keyword(s):  
Lagrange Interpolation

A Hierarchical Access Control Scheme Based on Lagrange Interpolation and ELGamal Algorithm with Numerical Experiments

2013 ◽  
Vol 385-386 ◽  
pp. 1705-1707
Author(s):  
Tzer Long Chen ◽  
Yu Fang Chung ◽  
Jian Mao Hong ◽  
Jeng Hong Jhong ◽  
Chin Sheng Chen ◽  
...  
Keyword(s):  
Access Control ◽  
Lagrange Interpolation ◽  
Control Mechanism ◽  
Key Generation ◽  
Electronic Documents ◽  
Control Scheme ◽  
Video Systems ◽  
Efficient Scheme ◽  
On Line ◽  
Access Control Mechanism

It is important to notice that the access control mechanism has been widely applied in various areas, such as on-line video systems, wireless network, and electronic documents. We propose an access control mechanism which is constructed based on two mathematical fundamentals: Lagrange interpolation and ElGamal algorithm. We conduct performance analysis to compare the efficiency of our proposed scheme with that of several related published schemes in both key generation phase and key derivation phase. Our new scheme is proven to be more efficient. It is shown, as expected, a more efficient scheme provides relatively less security and a more secure scheme is relatively less efficient for private keys of the same size.

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