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Accurate Computation of Gaussian Quadrature for Tension Powers (CROSBI ID 532963)

Prilog sa skupa u zborniku | izvorni znanstveni rad | međunarodna recenzija

Singer, Saša Accurate Computation of Gaussian Quadrature for Tension Powers // 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 (NY): American Institute of Physics (AIP), 2007. str. 515-518-x

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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nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

nije evidentirano

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

Povezanost rada

Matematika