Gauss-Legendre points

In the quantum calculations the number of included Fourier coefficients in the expansion of the paths was taken to be 1, and four Gauss-Legendre points were used in the u integrations. This number of coefficients and integration points was shown to be sufficient for Lennard-Jones argon. In both the classical and the quantum calculations the Metropolis box size was chosen so... 

For the radial part the Gauss-Legendre method was used for numerical integration of different functionals using 40 radial points. 

Gauss quadratures are numerical integration methods that employ Legendre points. Gauss quadrature cannot integrate a function given in a tabular form with equispaced intervals. It is expressed as ... 

For example, the Gauss-Legendre formula with three points is vaUd for the Interval [—1 1] and uses the points... 

For example, the Gauss-Legendre method a = -1, b = 1, four points and of order 8 requires the following values ... 

Gauss-Legendre quadrature, there are typically only about a third as many quadrature points as finite difference grid points. In addition, these quadratures... 

For each symmetry, then, the DVR basis is the direct product of equally spaced points in p. Gauss associated Legendre points in 6, and the eigenvalues of cos 6x in the appropriate symmetry basis of polynomials in cos For each syimnetry (e.g. A2) the... 

From a numerical point of view step (1) is not difficult if one applies the Gauss-Legendre method to the oscillatory integrand (due to the... 

As our angular grid points we use the Gauss-Legendre quadrature points. The grid representation of the wavefunction, is... 

Nquad — 40 for all subsequent scattering calculations to ensure that exact integration is obtained (provided that tg = 50). We note that Gauss-Legendre quadrature with 40 points exactly integrates a polynomial of degree 80, which is precisely the Newton polynomial used. 

Subroutine GAULEG(XX,WW,NDVR) gives NDVR Gauss-Legendre quadrature points XX(1 NDVR) and the corresponding weights WW(1 NDVR). 

C N - Extra parameter NDVR = N+NFUN becomes a number of quadrature C points in Gauss-Legendre integration, must not exceed NDIM... 

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