## 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.

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### Key words

reduction, polynomials, approximation, Bézier curves

### AMS subject classifications

41A10, 65D05, 65D17

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