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rSPDE is used for approximating fractional elliptic SPDEs $$L^\beta (\tau u(s)) = W,$$ where \(L\) is a differential operator and \(\beta>0\) is a general fractional power.


The approximation is based on a rational approximation of the fractional operator, and allows for computationally efficient inference and simulation.

The main functions for computing rational approximation objects are:


works for general rational operators


works for random fields with stationary Matern covariance functions


works for random fields with defined as solutions to a possibly non-stationary Matern-type SPDE model.


R-INLA implementation of the covariance-based rational approximation for random fields with stationary Matern covariance functions

Basic statistical operations such as likelihood evaluations (see [rSPDE.loglike], [rSPDE.matern.loglike]) and kriging predictions (see [predict.rSPDEobj], [predict.CBrSPDEobj]) using the rational approximations are also implemented.

For illustration purposes, the package contains a simple FEM implementation for models on R. For spatial models, the FEM implementation in the R-INLA package is recommended.

For a more detailed introduction to the package, see the rSPDE Vignettes.


Maintainer: David Bolin


Other contributors: