Gauss quadrature algorithm

In order to eliminate the restriction of evenly spaced points. Gauss Quadrature algorithms may be constructed. In these algorithms not only the function values are weighted, but the position of the function evaluations as well as the set of weight factors are left as parameters to be determined by optimizing the overall... 

All quadratures were done by means of the Gauss-Hermite algorithm. 

These algorithms are frequently stated in terms of integrals over [-1,1], termed Gauss-Legendre quadrature, and the general formula then is... 

Of the most common implicit algorithms, the most useful ones are those adopting quadrature points, which are points used by the open Gauss method, semiopen Radau method, and the close Lobatto method (see Chapter 1). 

Arasaratnam I et al (2007) Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature. Proc IEEE 95 953-977... 

Matrix in Golub-Welsch algorithm for which the eigensys-tem are the Gauss-Lobatto quadrature points and weights Product difference matrix of order (2Nq- -l)(2Nq- -l) in PD algorithm... 

In this section, the accuracy of the sparse grid collocation technique for computing numerically multidimensional integrals is examined. A test function is examined whose exact numerical integral is available. For the one-dimensional quadrature rules used in the Smolyak s algorithm, only the nested quadrature rules, namely, the Clenshaw-Curtis(CC) rule and the Gauss-Patterson(GP) rule, have been used. 

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