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Computes Gauss-Hermite quadrature rule of requested order using Golub-Welsch algorithm. Returns result in list consisting of two entries: x, for nodes, and w, for quadrature weights. This is very fast and numerically stable, using the Golub-Welsch algorithm with specialized eigendecomposition (symmetric tridiagonal) LAPACK routines. It can handle quadrature of order 1000+.
● Data Source:
CranContrib
● Keywords: math
● Alias: gaussHermiteData
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evalHermitePoly
(Package: fastGHQuad) :
Evaluate Hermite polynomial at given location
Evaluate Hermite polynomial of given degree at given location. This function is provided for demonstration/teaching purposes; this method is not used by gaussHermiteData. It is numerically unstable for high-degree polynomials.
● Data Source:
CranContrib
● Keywords: math
● Alias: evalHermitePoly
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aghQuad
(Package: fastGHQuad) :
Adaptive Gauss-Hermite quadrature using Laplace approximation
Convenience function for integration of a scalar function g based upon its Laplace approximation.
● Data Source:
CranContrib
● Keywords: math
● Alias: aghQuad
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fastGHQuad-package
(Package: fastGHQuad) :
A package for fast, numerically-stable computation of Gauss-Hermite
This package provides functions to compute Gauss-Hermite quadrature rules very quickly with a higher degree of numerical stability (tested up to 2000 nodes).
● Data Source:
CranContrib
● Keywords: package
● Alias: fastGHQuad, fastGHQuad-package
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findPolyRoots
(Package: fastGHQuad) :
Find real parts of roots of polynomial
Finds real parts of polynomial's roots via eigendecomposition of companion matrix. This method is not used by gaussHermiteData. Only the real parts of each root are retained; this can be useful if the polynomial is known a priori to have all roots real.
● Data Source:
CranContrib
● Keywords: math
● Alias: findPolyRoots
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ghQuad
(Package: fastGHQuad) :
Convenience function for Gauss-Hermite quadrature
Convenience function for evaluation of Gauss-Hermite quadrature
● Data Source:
CranContrib
● Keywords: math
● Alias: ghQuad
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hermitePolyCoef
(Package: fastGHQuad) :
Get coefficient of Hermite polynomial
Calculate coefficients of Hermite polynomial using recursion relation. This function is provided for demonstration/teaching purposes; this method is not used by gaussHermiteData. It is numerically unstable for high-degree polynomials.
● Data Source:
CranContrib
● Keywords: math
● Alias: hermitePolyCoef
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