You are here

Home » Content

Generalized Tschebyscheff of the Second Kind and Bernstein Polynomials Change of Bases

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2015

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
We construct multiple representations relative to different bases of the generalized Tschebyscheff polynomials of second kind. Also, we provide an explicit closed from of The generalized Polynomials of degree r less than or equal n in terms of the Bernstein basis of fixed degree n. In addition, we create the change-of-basis matrices between the generalized Tschebyscheff of the second kind polynomial basis and Bernstein polynomial basis.
Bookmark/Search this post with
FULL TEXT (PDF): 
PDF icon 2434-5560-1-pb.pdf
  • 3
324
331
  • English

REFERENCES

References: 

[1] M. AlQudah. The generalized Tschebyscheff polynomials of the second kind. Turkish Journal
of Mathematics, 39. http://dx.doi.org/10.3906/mat-1501-44. 2015.
[2] R. Farouki. The Bernstein polynomial basis: A centennial retrospective. Computer Aided
Geometric Design, 29(6), 379–419. 2012.
[3] R. Farouki and V. Rajan. Algorithms for polynomials in Bernstein form. Computer Aided
Geometric Design, 5(1), 1–26. 1988.
[4] I. Gradshtein and I. Ryzhik. Tables of integrals, series, and products. Academic Press, New
York. 1980.
[5] T. Koornwinder. Orthogonal polynomials with weight function (1− x)(1+ x) +M(x +
1) + N(x − 1). Canadian Mathematical Bulletin, 27(2), 205–214. 1984.
[6] A. Rababah. Transformation of Chebyshev Bernstein polynomial basis. Computational
Methods in Applied Mathematics, 3(4), 608–622. 2003.
[7] J. Rice. The Approximation of Functions, Linear Theory. Vol. 1. Addison-Wesley, Reading,
Mass. 1964.
[8] G. Szegö. Orthogonal polynomials. American Mathematical Society Colloquium Vol. 23,
4th ed. Providence, RI: American Mathematical Society. 1975.

Thank you for copying data from http://www.arastirmax.com