Accurate Computation of Gaussian Quadrature for Tension Powers (CROSBI ID 532963)
Prilog sa skupa u zborniku | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Singer, Saša
engleski
Accurate Computation of Gaussian Quadrature for Tension Powers
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.
tension powers; tension splines; Gaussian quadrature; nodes; weights; accuracy; efficiency
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Podaci o prilogu
515-518-x.
2007.
objavljeno
Podaci o matičnoj publikaciji
AIP Conf. Proc. -- Volume 936 NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference of Numerical Analysis and Applied Mathematics
Simos, Theodoros ; Psihoyios, George ; Tsitouras, Ch.
Melville (NY): American Institute of Physics (AIP)
978-0-7354-0447-2
Podaci o skupu
International Conference of Numerical Analysis and Applied Mathematics 2007
predavanje
16.09.2007-20.09.2007
Krf, Grčka