| mvQuad-package {mvQuad} | R Documentation |
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.
Details
| Package: | mvQuad |
| Type: | Package |
| Version: | 1.0-8 |
| Date: | 2023-09-18 |
| License: | GPL-3 |
Author(s)
Constantin Weiser (University Mainz / Germany) Maintainer: Constantin Weiser <constantin.weiser@gmail.com>
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)