Legendre-Bernstein basis transformations

Journal of Computational and Applied Mathematics

Volumn 119, Issue 1-2, 2000, Pages 145-160

  Farouki, Rida T ^a  

^a University of California   (United States)

Author keywords

Basis transformations; Bernstein basis; Condition numbers; Least squares approximations; Legendre basis; Orthogonal polynomials

Indexed keywords

ALGORITHMS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; POLYNOMIALS;

LEGENDRE-BERNSTEIN BASIS TRANSFORMATION;

COMPUTATIONAL GEOMETRY;

EID: 0033718742     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(00)00376-9     Document Type: Article

References (20)

1. Chihara T.S. An Introduction to Orthogonal Polynomials. 1978;Gordon and Breach, New York.
2. Davis P.J. Interpolation and Approximation. 1975;Dover, New York.
3. Farin G. Curves and Surfaces for CAGD, 3rd ed. 1993;Academic Press, Boston.
4. H.W. Gould, Combinatorial Identities, Morgantown, West Virginia, 1972.
5. R.L. Graham, D.E. Knuth, O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1989.
6. Isaacson E., Keller H.B. Analysis of Numerical Methods. 1994;Dover, New York.
7. D.E. Knuth, The Art of Computer Programming, Vol. 1 Fundamental Algorithms, 2nd ed., Addison-Wesley, Reading, MA, 1973.
8. Stewart G.W. Introduction to Matrix Computations. 1973;Academic Press, New York.
9. G. Szegö, Orthogonal Polynomials, 4th ed., American Mathematical Society, Providence, RI, 1975.
10. Daniel M., Daubisse J.C. The numerical problem of using Bézier curves and surfaces in the power basis. Comput. Aided Geom. Design. 6:1989;121-128.
11. Farouki R.T. On the stability of transformations between power and Bernstein polynomial forms. Comput. Aided Geom. Design. 8:1991;29-36.
12. Farouki R.T. Convergent inversion approximations for polynomials in Bernstein form. Comput. Aided Geom. Design. 17:2000;179-196.
13. Farouki R.T., Goodman T.N.T. On the optimal stability of the Bernstein basis. Math. Comp. 65:1996;1553-1566.
14. Farouki R.T., Neff C.A. On the numerical condition of Bernstein-Bézier subdivision processes. Math. Comp. 55:1990;637-647.
15. Farouki R.T., Rajan V.T. On the numerical condition of polynomials in Bernstein form. Comput. Aided Geom. Design. 4:1987;191-216.
16. Farouki R.T., Rajan V.T. Algorithms for polynomials in Bernstein form. Comput. Aided Geom. Design. 5:1988;1-26.
17. Hermann T. On the stability of polynomial transformations between Taylor, Bézier, and Hermite forms. Numer. Algorithms. 13:1996;307-320.
18. Jüttler B. The dual basis functions for the Bernstein polynomials. Adv. Comput. Math. 8:1998;345-352.
19. Li Y-M., Zhang X-Y. Basis conversion among Bézier, Tchebyshev, and Legendre. Comput. Aided Geom. Design. 15:1998;637-642.
20. D.E. Knuth, personal communication, 1999.