본문 바로가기
KERD
논문KCI 등재

Constrained Jacobi polynomial and constrained Chebyshev polynomial

안영준
대한수학회 (The Korean Mathematical Society)|2008.04|대한수학회논문집 (Communications of the KMS)|제23권 제2호|pp. 279-284

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

Jacobi polynomialChebyshev polynomialdegree reductionC0 constraint.
주제분류수학

초록

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n = 4, 5, we find the constrained Jacobi polynomial, and for n ≥ 6, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

Abstract

In this paper, we present the constrained Jacobi polynomial which is equal to the constrained Chebyshev polynomial up to constant multiplication. For degree n = 4, 5, we find the constrained Jacobi polynomial, and for n ≥ 6, we present the normalized constrained Jacobi polynomial which is similar to the constrained Chebyshev polynomial.

참고문헌 (20)

  1. Y. J. Ahn, "Degree reduction of B´ezier curves with Ck-continuity using Jacobi polynomials", Comp. Aided Geom. Desi, 20, pp.423~434 (2003)
  2. Y. J. Ahn, "Degree reduction of Bezier curves using constrained Chebyshev polynomials of second kind", ANZIAM J, 45, pp.195~205 (2003)
  3. Y. J. Ahn, "Constrained polynomial degree reduction in the L2-norm equals best weighted Euclidean approximation of B´ezier coefficients", Comp. Aided Geom. Desi, 21, pp.181~191 (2004)
  4. T. S. Chihara, "An introduction to orthogonal polynomials" (1978), Gordon and Breach
  5. P. J. Davis, "Interpolation and approximation" (1975), Dover publications
  6. M. Eck, "Degree reduction of B´ezier curves", Comp. Aided Geom. Desi, 10, pp.237~251 (1993)
  7. M. Eck, "Least squares degree reduction of B´ezier curves", Computer-Aided Design, 27, pp.845~851 (1995)
  8. H. J. Kim, "Good degree reduction of B´ezier curves using Jacobi polynomials", Comp. Math. Appl, 40, pp.1205~1215 (2000)
  9. H. O. Kim, "Degree reduction of B´ezier curves and filter banks", Comp. Math. Appl, 31, pp.23~30 (1996)
  10. H. S. Kim, "Constrained degree reduction of polynomials in Bernstein Bezier form over simplex domain", Journal of Computational and Applied Mathematics (2007)
  11. M. A. Lachance, "Chebyshev economization for parametric surfaces", Comp. Aided Geom. Desi, 5, pp.195~208 (1988)
  12. M. A. Lachance, "Approximation by constrained parametric polynomials", Rocky Mountain J. Math, 21, pp.473~488 (1991)
  13. B. G. Lee, "Distance for B´ezier curves and degree reduction", Bull. Australian Math. Soc, 56, pp.507~515 (1997)
  14. B. G. Lee, "Application of Legendre-Bernstein basis transformations to degree elevation and degree reduction", Comp. Aided Geom. Desi, 19, pp.709~718 (2002)
  15. D. Lutterkort, "Polynomial degree reduction in the L2-norm equals best Euclidean approximation of B´ezier coefficients", Comp. Aided Geom. Desi, 16, pp.607~612 (1999)
  16. J. Peters, "Least squares approximation of B´ezier coefficients provides best degree reduction in the L2-norm", J. Approximation Theory, 104, pp.90~97 (2000)
  17. H. Sunwoo, "A unified matrix representation for degree reduction of Bezier curves", Comp. Aided Geom. Desi, 21, pp.151~164 (2004)
  18. H. Sunwoo, "Matrix representation for multi-degree reduction of Bezier curves", Comp. Aided Geom. Desi, 22, pp.261~273 (2005)
  19. G. Szego, "Orthogonal polynomials", AMS Coll. Publ, 23
  20. M. Watkins, "Degree reduction for B´ezier curves", Computer-Aided Design, 20, pp.398~405 (1988)

관련 논문AI추천

SUMS OF FINITE PRODUCTS OF LEGENDRE AND LAGUERRE POLYNOMIALS BY CHEBYSHEV POLYNOMIALS권종겸, 김대산, 김태균, 장관우장전수학회 · Advanced Studies in Contemporary Mathematics2018 · 제28권 제4호Generalized Chebyshev polynomials of third kindAbedallah Rababah, Esraa Hijazi장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2018 · 제21권 제3호A note on q-Bernstein and q-Laguerre polynomialsB. Lee, C. S. Ryoo, D. V. Dolgy, T. Kim장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2011 · 제14권 제3호New connection formulae between ultraspherical polynomials and Chebyshev polynomials of third and fourth kindsE. H. Doha장전수학회 · Advanced Studies in Contemporary Mathematics2015 · 제25권 제4호On difference quotients of Chebyshev polynomials김선홍, Jung Hee Lee대한수학회 · 대한수학회보2016 · 제53권 제2호On Finite Integrals Involving JacobiPolynomials and the -functionRajendra P. Sharma경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2006 · 제46권 제3호

이 간행물의 다른 논문 (15건)

Notes on a non-associative algebras with exponential functions III최설희pp. 153-159On potent ringsBingjun Lipp. 161-167TOPOLOGICAL PROPERTIES IN BCC-ALGEBRAS안선신, 권석환pp. 169-178A note on lacunary statistically convergent double sequences of fuzzy numbersYavuz Altinpp. 179-185A reducibility of Exton's triple hypergeometric series X₂Arjun K. Rathie, 최준상pp. 187-189
원문 보기