mvQuad (version 1.0-8)

mvQuad-package: Methods for multivariate Quadrature (numerical integration)

Description

This package 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-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.

Author

Constantin Weiser (University Mainz / Germany) Maintainer: Constantin Weiser <[e-mail]>

Details

Package:	mvQuad
Type:	Package
Version:	1.0-8
Date:	2023-09-18
License:	GPL-3

References

Philip J. Davis, Philip Rabinowitz (1984): Methods of Numerical Integration

F. Heiss, V. Winschel (2008): Likelihood approximation by numerical integration on sparse grids, Journal of Econometrics

H.-J. Bungartz, M. Griebel (2004): Sparse grids, Acta Numerica

Peter Jaeckel (2005): A note on multivariate Gauss-Hermite quadrature

Examples

myGrid <- createNIGrid(dim=2, type="GLe", level=5)
rescale(myGrid, domain=rbind(c(-1,1),c(-1,1)))
print(myGrid)
plot(myGrid, col="blue")
myFun <- function(x){
   1 - x[,1]^2 * x[,2]^2
}
quadrature(myFun, myGrid)