QuadRules

This data set stores nodes an weights for Gauss-Quadrature.
 Syntax:
QuadRules[['type']][['level']]<ul>
<li>type="GLe" Gauss-Legendre; interval [0,1]; max-level 45</li>
<li>type="nLe" nested-type Gauss-Legendre; interval [0,1]; max-level 25</li>
<li>type="GKr" Gauss-Kronrod; interval [0,1]; max-level 29</li>
<li>type="GLa" Gauss-Laguere; interval [0, Inf); max-level 30</li>
<li>type="GHe" Gauss-Hermite; interval (-Inf, Inf); max-level 45</li>
<li>type="GHN" Gauss-Hermite (as above, but pre-multiplied weights \(\hat(w)_i = w_i * \phi(x_i)\))</li>
<li>type="nHe" nested-type Gauss-Hermite; interval (-Inf, Inf) max-level 25</li>
<li>type="nHN" nested-type Gauss-Hermite (as above, but pre-multiplied weights \(\hat(w)_i = w_i * \phi(x_i)\))</li>
<li>type="Leja" Leja-points; interval [0,1]; max-level 141</li>
</ul>

datasets

Provides methods to construct multivariate grids, which can be used
for multivariate quadrature. This grids can be based on different quadrature
rules like Newton-Cotes formulas (trapezoidal-, Simpson's- rule, ...) or Gauss
quadrature (Gauss-Hermite, Gauss-Legendre, ...). For the construction of the
multidimensional grid the product-rule or the combination- technique can be
applied.

Constantin Weiser

mvQuad

Methods for Multivariate Quadrature

QuadRules function

list of nodes and weights (for organisation see "Syntax" in description section)

Format

This data set stores nodes an weights for Gauss-Quadrature.
 Syntax:
QuadRules[['type']][['level']]

<ul>
<li>type="GLe" Gauss-Legendre; interval [0,1]; max-level 45</li>
<li>type="nLe" nested-type Gauss-Legendre; interval [0,1]; max-level 25</li>
<li>type="GKr" Gauss-Kronrod; interval [0,1]; max-level 29</li>
<li>type="GLa" Gauss-Laguere; interval [0, Inf); max-level 30</li>
<li>type="GHe" Gauss-Hermite; interval (-Inf, Inf); max-level 45</li>
<li>type="GHN" Gauss-Hermite (as above, but pre-multiplied weights \(\hat(w)_i = w_i * \phi(x_i)\))</li>
<li>type="nHe" nested-type Gauss-Hermite; interval (-Inf, Inf) max-level 25</li>
<li>type="nHN" nested-type Gauss-Hermite (as above, but pre-multiplied weights \(\hat(w)_i = w_i * \phi(x_i)\))</li>
<li>type="Leja" Leja-points; interval [0,1]; max-level 141</li>
</ul>

QuadRules: nodes and weights for 1D - Gauss-Quadrature

Description

Arguments

Format

Examples