S. Hamaguchi, R.T. Farouki
The Journal of Chemical Physics
We show that in the ||{radical dot}||1 and ||{radical dot}||∞ norms, the condition number of the matrix T that maps the coefficients of a polynomial P(t) of degree n in the Bernstein basis on t ∈[0,1] to those in the power basis about t = 0, or vice-versa, assumes the simple form κ(T) = (n+1)(nν)2ν where ν denotes the largest integer not exceeding 2(n + 1)/3 (for n ≥ 3, the expression κ(T){reversed tilde equals}3n+1 n + 1 2 π gives an excellent approximation). The growth of κ(T) with n suggests a potentially severe loss of accuracy during the basis conversion of high-degree curves and surfaces, a practice that should be avoided whenever possible. © 1991.
S. Hamaguchi, R.T. Farouki
The Journal of Chemical Physics
R.T. Farouki, C. Neff, et al.
ACM Transactions on Graphics (TOG)
S. Hamaguchi, R.T. Farouki
ICOPS 1994
R.T. Farouki, S. Hamaguchi, et al.
Physical Review A