A modified Gaussian quadrature rule for integrals involving poles of any order

1986 ◽  
Vol 26 (2) ◽  
pp. 233-240 ◽  
Author(s):  
D. B. Hunter ◽  
G. E. Okecha
Keyword(s):  
Gaussian Quadrature ◽  
Quadrature Rule ◽  
Gaussian Quadrature Rule

Gaussian quadrature rule for arbitrary weight function and interval

2005 ◽  
Vol 167 (2) ◽  
pp. 143-150 ◽  
Author(s):  
H. Fukuda ◽  
M. Katuya ◽  
E.O. Alt ◽  
A.V. Matveenko
Keyword(s):  
Weight Function ◽  
Gaussian Quadrature ◽  
Quadrature Rule ◽  
Arbitrary Weight ◽  
Gaussian Quadrature Rule

scholarly journals A Novel Algorithm to Evaluate Definite Integrals by the Gauss-Legendre Integration Rule Based on the Stochastic Arithmetic: Application in the Model of Osmosis System

2020 ◽  
Vol 7 (4) ◽  
pp. 577-586
Author(s):  
Samad Noeiaghdam ◽  
Mohammad Ali Fariborzi Araghi
Keyword(s):  
Gaussian Quadrature ◽  
Computer Arithmetic ◽  
Quadrature Rule ◽  
Integration Rule ◽  
Rule Based ◽  
Stochastic Arithmetic ◽  
Definite Integrals ◽  
Improper Integral ◽  
The Common ◽  
Gaussian Quadrature Rule

Finding the optimal iteration of Gaussian quadrature rule is one of the important problems in the computational methods. In this study, we apply the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library to find the optimal iteration and optimal approximation of the Gauss-Legendre integration rule (G-LIR). A theorem is proved to show the validation of the presented method based on the concept of the common significant digits. Applying this method, an improper integral in the solution of the model of the osmosis system is evaluated and the optimal results are obtained. Moreover, the accuracy of method is demonstrated by evaluating other definite integrals. The results of examples illustrate the importance of using the stochastic arithmetic in discrete case in comparison with the common computer arithmetic.

scholarly journals A Gaussian quadrature rule for oscillatory integrals on a bounded interval

2014 ◽  
Vol 34 (3) ◽  
pp. 883-901 ◽  
Author(s):  
Andreas Asheim ◽  
◽  
Alfredo Deaño ◽  
Daan Huybrechs ◽  
Haiyong Wang
Keyword(s):  
Gaussian Quadrature ◽  
Quadrature Rule ◽  
Oscillatory Integrals ◽  
Bounded Interval ◽  
Gaussian Quadrature Rule

scholarly journals Influence of phase noise and interchannel interference on the performance of optical heterodyne FSK receiver

2003 ◽  
Vol 1 (1) ◽  
pp. 111-121
Author(s):  
Mihajlo Stefanovic ◽  
D. Milic
Keyword(s):  
Phase Noise ◽  
Error Probability ◽  
Gaussian Quadrature ◽  
Quadrature Rule ◽  
Optical Systems ◽  
Optical Heterodyne ◽  
Channel Spacing ◽  
Interchannel Interference ◽  
The Matrix ◽  
Gaussian Quadrature Rule

The moments approach is generally considered a systematic way to perform the analysis of coherent optical systems. Exact moments of the filtered signal corrupted by phase noise enable the construction of the Gaussian quadrature rule, which may be used to calculate the system error probability. In this paper, we extend the method to a wider class of systems to include the cases where the interchannel interference may be significant. We derive the essential equations in the matrix form and compare the moments approach with numerical simulation and Fokker-Planck approach. To illustrate the results, we apply the moment's method to two-channel optical heterodyne FSK system with dual-filter receiver structure, and evaluate the required channel spacing to have less than 1 dB penalty due to crosstalk.

Sign in / Sign up

Export Citation Format

Share Document