Geodesic
Polynomial best constrained degree reduction in strain energy
Electronic transactions on numerical analysis, Tome 26 (2007), pp. 312-319
We exhibit the best degree reduction of a given degree polynomial by minimizing the strain energy $\textcent $of the error with the constraint that continuity of a prescribed order is preserved at the two endpoints. It is shown that a multidegree reduction is equivalent to a step-by-step reduction of one degree at a time by using the Fourier coefficients with respect to Jacobi orthogonal polynomials. Then we give explicitly the optimal constrained one degree reduction in B$\acute $ezier form, by perturbing the B$\acute $ezier coefficients.
Classification : 41A10, 65D05, 65D17
Keywords: reduction, polynomials, approximation, B$\acute $ezier curves 
@article{ETNA_2007__26__a8,
     author = {Randriambelosoa,  Germain E.},
     title = {Polynomial best constrained degree reduction in strain energy},
     journal = {Electronic transactions on numerical analysis},
     pages = {312--319},
     year = {2007},
     volume = {26},
     zbl = {1176.41013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__26__a8/}
}
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EP  - 319
VL  - 26
UR  - http://geodesic.mathdoc.fr/item/ETNA_2007__26__a8/
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%A Randriambelosoa,  Germain E.
%T Polynomial best constrained degree reduction in strain energy
%J Electronic transactions on numerical analysis
%D 2007
%P 312-319
%V 26
%U http://geodesic.mathdoc.fr/item/ETNA_2007__26__a8/
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%F ETNA_2007__26__a8
Randriambelosoa,  Germain E. Polynomial best constrained degree reduction in strain energy. Electronic transactions on numerical analysis, Tome 26 (2007), pp. 312-319. http://geodesic.mathdoc.fr/item/ETNA_2007__26__a8/