Bivariate Lagrange interpolation based on Chebyshev points of the second kind

2019 ◽  
Vol 159 (2) ◽  
pp. 618-637
Author(s):  
J. Liu ◽  
L. Y. Zhu
Keyword(s):  
Lagrange Interpolation ◽  
Chebyshev Points

scholarly journals Upper Bound for Lebesgue Constant of Bivariate Lagrange Interpolation Polynomial on the Second Kind Chebyshev Points

2022 ◽  
Vol 2022 ◽  
pp. 1-19
Author(s):  
Juan Liu ◽  
Laiyi Zhu
Keyword(s):  
Upper Bound ◽  
Chebyshev Polynomials ◽  
Lagrange Interpolation ◽  
Lebesgue Constant ◽  
Interpolation Polynomial ◽  
Growth Order ◽  
Lagrange Interpolation Polynomial ◽  
Chebyshev Points ◽  
The Common ◽  
Common Zeros

In the paper, we study the upper bound estimation of the Lebesgue constant of the bivariate Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the second kind on the square − 1,1 2 . And, we prove that the growth order of the Lebesgue constant is O n + 2 2 . This result is different from the Lebesgue constant of Lagrange interpolation polynomial on the unit disk, the growth order of which is O n . And, it is different from the Lebesgue constant of the Lagrange interpolation polynomial based on the common zeros of product Chebyshev polynomials of the first kind on the square − 1,1 2 , the growth order of which is O ln n 2 .

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.

scholarly journals Local Lagrange interpolation using cubic C1 splines on type-4 cube partitions

2010 ◽  
Vol 162 (3) ◽  
pp. 494-511 ◽  
Author(s):  
Michael A. Matt ◽  
Günther Nürnberger
Keyword(s):  
Lagrange Interpolation

scholarly journals Barycentric Lagrange Interpolation

SIAM Review ◽  
2004 ◽  
Vol 46 (3) ◽  
pp. 501-517 ◽  
Author(s):  
Jean-Paul Berrut ◽  
Lloyd N. Trefethen
Keyword(s):  
Lagrange Interpolation
Sign in / Sign up

Export Citation Format

Share Document