Abstract
The stability of transformations between Taylor and Hermite and Bernstein and Hermite forms of the polynomials are investigated. The results are analogous to Farouki's concerning the stability of the transformation between Taylor and Bernstein form. An exact asymptotic is given for the condition numbers in thel 1 case.
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References
P. Charrot, The use of triangular and pentagonal patches in the numerical representation of surfaces, Ph. D. thesis, Department of Mathematics, Brunel University (1980).
M. Daniel and J. C. Daubisse, The numerical problem of using Bézier curves and surfaces in the power basis, Computer Aided Geometric Design 6 (1989) 121–128.
R. T. Farouki, On the stability of transformations between power and Bernstein polynomial forms, Computer Aided Geometric Design 8 (1991) 29–36.
R. T. Farouki and V. T. Rajan, On the numerical condition of polynomials in Bernstein form, Computer Aided Geometric Design 4 (1987) 191–216.
D. E. Knuth,The Art of Computer Programming I (Addison-Wesley, 1981).
G. W. Stewart,Introduction to Matrix Computations (Academic Press, 1973).
J. H. Wilkinson,The Algebraic Eigenvalue Problem (Clarendon Press, Oxford, 1988).
A. Zygmund,Trigonometric Series (University Press, Cambridge, 1959).
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Communicated by G. Mühlbach
Research was partially supported by the Copernicus grant RECCAD 94-1068 and by the National Research Foundation of the Hungarian Academy of Sciences grant 16420.