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## Accurate Computation of Gaussian Quadrature for Tension Powers

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, New York: American Institute of Physics, 2007. str. 515-518 (predavanje, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)

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Naslov
Accurate Computation of Gaussian Quadrature for Tension Powers

Autori
Singer, Saša

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. - 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

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Projekti:
037-1193086-2771 - Numeričke metode u geofizičkim modelima (Singer, Saša, MZOS ) ( POIROT)

Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb

#### Citiraj ovu publikaciju:

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, New York: American Institute of Physics, 2007. str. 515-518 (predavanje, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)
Singer, S. (2007) Accurate Computation of Gaussian Quadrature for Tension Powers. U: Simos, T., Psihoyios, G. & Tsitouras, C. (ur.)AIP Conf. Proc. -- Volume 936 NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference of Numerical Analysis and Applied Mathematics.
@article{article, author = {Singer, Sa\v{s}a}, year = {2007}, pages = {515-518}, keywords = {tension powers, tension splines, Gaussian quadrature, nodes, weights, accuracy, efficiency}, isbn = {978-0-7354-0447-2}, title = {Accurate Computation of Gaussian Quadrature for Tension Powers}, keyword = {tension powers, tension splines, Gaussian quadrature, nodes, weights, accuracy, efficiency}, publisher = {American Institute of Physics}, publisherplace = {Krf, Gr\v{c}ka} }
@article{article, author = {Singer, Sa\v{s}a}, year = {2007}, pages = {515-518}, keywords = {tension powers, tension splines, Gaussian quadrature, nodes, weights, accuracy, efficiency}, isbn = {978-0-7354-0447-2}, title = {Accurate Computation of Gaussian Quadrature for Tension Powers}, keyword = {tension powers, tension splines, Gaussian quadrature, nodes, weights, accuracy, efficiency}, publisher = {American Institute of Physics}, publisherplace = {Krf, Gr\v{c}ka} }

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