On The Shape Preserving Approximation: Constrained and Unconstrained Approximation - Eman Bhaya,Halgwrd Darwesh
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Toimitus 12-18 arkipäivässä
30 päivän palautusoikeus
Sometimes one may desire to approximate a function defined on a finite interval (for example [-1,1]), subject to the conservation of so called shape properties (positivity, monotonicity and convexity). The first contribution is that we have approximated a function from a space Lp[-1,1], 0 > p, by a number of piecewise linear functions and we have obtained global estimate of each of them using the second ... Täydellinen kuvaus
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Kuvaus
Sometimes one may desire to approximate a function defined on a finite interval (for example [-1,1]), subject to the conservation of so called shape properties (positivity, monotonicity and convexity). The first contribution is that we have approximated a function from a space Lp[-1,1], 0 > p, by a number of piecewise linear functions and we have obtained global estimate of each of them using the second order of Ditzian ¿ Totik modulus of smoothness. Furthermore, these piecewise linear functions preserves the positivity of the function. Also proved the rate of coconvex approximation in the Lp[-1,1] spaces, in terms of the third order of Ditzian ¿ Totik modulus of smoothness, where the constants involved depend on the location of the points of change of convexity. We have thus filled up a gap due to the uncertainty between previously known estimates involving the second order of Ditzian ¿ Totik modulus of smoothness and the impossibility of having such estimates involving with the second order of usual modulus of smoothness.
Lisätietoja
| Kirjoittaja | Eman Bhaya, Halgwrd Darwesh |
|---|---|
| Julkaisija | LAP LAMBERT Academic Publishing |
| Julkaisuvuosi | 2011 |
| Kannen tyyppi | Pehmeäkantinen |
| EAN | 9783846524671 |