Volume 26, pp. 312-319, 2007.
Polynomial best constrained degree reduction in strain energy
Germain E. Randriambelosoa
Abstract
We exhibit the best degree reduction of a given degree polynomial by minimizing
the strain energy of the error with the constraint that continuity of a prescribed
order is preserved at the two endpoints. It is shown that a multidegree reduction
is equivalent to a step-by-step reduction of one degree at a time by using the Fourier
coefficients with respect to Jacobi orthogonal polynomials. Then we give explicitly
the optimal constrained one degree reduction in Bézier form, by perturbing the Bézier
coefficients.
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Key words
reduction, polynomials, approximation, Bézier curves
AMS subject classifications
41A10, 65D05, 65D17
