Naslov
Algebraic Proof of the B-spline Derivative Formula

Autori
Rogina, Mladen

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of the Conference on Applied Mathematics and Scientific Computing / Drmac, Zlatko ; Marusic, Miljenko ; Tutek, Zvonimir - : Springer, 2005, 273-281

Skup
Conference on Applied Mathematics and Scientific Computing, ApplMath03

Mjesto i datum
Brijuni, Hrvatska, 23.06.2003. - 27.06.2003

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Chebyshev splines; Divided differences

Sažetak
We prove a well known formula for the generalized derivatives of Chebyshev B--splines: \begin{; ; ; eqnarray*}; ; ; L_1B_i^k(x) & = & \frac{; ; ; B_i^{; ; ; k-1}; ; ; (x)}; ; ; {; ; ; C_{; ; ; k-1}; ; ; (i)}; ; ; - \frac{; ; ; B_{; ; ; i+1}; ; ; ^{; ; ; k-1}; ; ; (x)}; ; ; {; ; ; C_{; ; ; k-1}; ; ; (i+1)}; ; ; , \end{; ; ; eqnarray*}; ; ; where \begin{; ; ; eqnarray}; ; ; C_{; ; ; k-1}; ; ; (i) & = & \int_{; ; ; t_{; ; ; i}; ; ; }; ; ; ^{; ; ; t_{; ; ; i+k-1}; ; ; }; ; ; B_i^{; ; ; k-1}; ; ; (x) d\sigma, \end{; ; ; eqnarray}; ; ; in a purely algebraic fashion, and thus show that it holds for the most general spaces of splines. The integration is performed with respect to a certain measure associated in a natural way to the underlying Chebyshev system of functions. Next, we discuss the implications of the formula for some special spline spaces, with an emphasis on those that are not ssociated with ECC-systems.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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