scholarly journals Vandermonde matrices on Chebyshev points

1998 ◽  
Vol 283 (1-3) ◽  
pp. 205-219 ◽  
Author(s):  
A. Eisinberg ◽  
G. Franzé ◽  
P. Pugliese
Keyword(s):  
Vandermonde Matrices ◽  
Chebyshev Points

scholarly journals Multiplication of Polynomials using Discrete Fourier Transformation

2006 ◽  
Vol 14 (4) ◽  
pp. 121-128
Author(s):  
Krzysztof Treyderowski ◽  
Christoph Schwarzweller
Keyword(s):  
Fourier Transformation ◽  
Discrete Fourier Transformation ◽  
Vandermonde Matrices ◽  
Univariate Polynomials

Multiplication of Polynomials using Discrete Fourier Transformation In this article we define the Discrete Fourier Transformation for univariate polynomials and show that multiplication of polynomials can be carried out by two Fourier Transformations with a vector multiplication in-between. Our proof follows the standard one found in the literature and uses Vandermonde matrices, see e.g. [27].

scholarly journals Covering and separation of Chebyshev points for non-integrable Riesz potentials

2018 ◽  
Vol 46 ◽  
pp. 19-44 ◽  
Author(s):  
A. Reznikov ◽  
E. Saff ◽  
A. Volberg
Keyword(s):  
Riesz Potentials ◽  
Chebyshev Points

Inverses of Vandermonde Matrices

1964 ◽  
Vol 71 (4) ◽  
pp. 410 ◽  
Author(s):  
F. D. Parker
Keyword(s):  
Vandermonde Matrices

Fast factorization of rectangular Vandermonde matrices with Chebyshev nodes

2018 ◽  
Vol 81 (2) ◽  
pp. 547-559 ◽  
Author(s):  
Mykhailo Kuian ◽  
Lothar Reichel ◽  
Sergij V. Shiyanovskii
Keyword(s):  
Chebyshev Nodes ◽  
Vandermonde Matrices

Newton Interpolation in Fejer and Chebyshev Points

1989 ◽  
Vol 53 (187) ◽  
pp. 265 ◽  
Author(s):  
Bernd Fischer ◽  
Lothar Reichel
Keyword(s):  
Newton Interpolation ◽  
Chebyshev Points

Analyzing the Precision of Chebyshev Polynomial Fitting GPS Satellite Ephemeris

2013 ◽  
Vol 353-356 ◽  
pp. 3410-3413 ◽  
Author(s):  
Shao Feng Xie ◽  
Peng Fei Zhang ◽  
Li Long Liu
Keyword(s):  
Chebyshev Polynomial ◽  
Interpolation Node ◽  
Polynomial Fitting ◽  
Chebyshev Points ◽  
Precise Ephemeris ◽  
The Difference

Using Chebyshev polynomial to fit precise ephemeris of GPS, the nodes selection has a certain influence on the precision. In this paper we use 3 kinds of precise ephemeris ( IGF, IGR, IGU ) to analyze the difference precision of randomly selected interpolation node and Chebyshev points fitting orbit and compare the difference and precision of fitting orbit by 3 kinds of ephemeris and orbit provided by IGS. The result shows that using Chebyshev points to fit precise ephemeris, the precision of IGF and IGR can achieve mm levels, the precision of IGU can achieve cm levels.

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