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 $n$ 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.

Full Text (PDF) [174 KB]

Key words

reduction, polynomials, approximation, Bézier curves

AMS subject classifications

41A10, 65D05, 65D17

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