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Pregled bibliografske jedinice broj: 321005

Zbornik radova

Autori: Singer, Saša
Naslov: Accurate Computation of Gaussian Quadrature for Tension Powers
Izvornik: AIP Conf. Proc. -- Volume 936 NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference of Numerical Analysis and Applied Mathematics / Simos, Theodoros ; Psihoyios, George ; Tsitouras, Ch. (ur.). - Melville, New York : American Institute of Physics , 2007. 515-518 (ISBN: 978-0-7354-0447-2).
Skup: International Conference of Numerical Analysis and Applied Mathematics 2007
Mjesto i datum: Krf, Grčka, 16-20.9.2007.
Ključne riječi: tension powers; tension splines; Gaussian quadrature; nodes; weights; accuracy; efficiency
Sažetak:
We consider Gaussian quadrature formulas which exactly integrate a system of tension powers $1, x, x^2, \ldots , x^{;n - 3};, \sinh(px), \cosh(px)$, on a given interval $[a, b]$, where $n \geq 4$ is an even integer and $p > 0$ is a given tension parameter. In some applications it is essential that $p$ can be changed dynamically, and we need an efficient "on-demand" algorithm that calculates the nodes and weights of Gaussian quadrature formulas for many different values of $p$, which are not known in advance. It is an interesting numerical challenge to achieve the required full machine precision accuracy in such an algorithm, for all possible values of p. By exploiting various analytic and numerical techniques, we show that this can be done efficiently for all reasonably low values of $n$ that are of any practical importance.
Vrsta sudjelovanja: Predavanje
Vrsta prezentacije u zborniku: Cjeloviti rad (više od 1500 riječi)
Vrsta recenzije: Međunarodna recenzija
Projekt / tema: 037-1193086-2771
Izvorni jezik: ENG
Kategorija: Znanstveni
Znanstvena područja:
Matematika
URL Internet adrese: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=936&Issue=1
Upisao u CROSBI: Sanja Singer (sanja.singer@fsb.hr), 6. Vel. 2008. u 20:13 sati



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