  Numerical computation of the Karhunen--Lo\`eve expansion is computationally
challenging in terms of both memory requirements and computing time. We compare
two state-of-the-art methods that claim to efficiently solve for the K--L
expansion: (1) the matrix-free isogeometric Galerkin method using interpolation
based quadrature proposed by the authors in [1] and (2) our new matrix-free
implementation of the isogeometric collocation method proposed in [2]. Two
three-dimensional benchmark problems indicate that the Galerkin method performs
significantly better for smooth covariance kernels, while the collocation
method performs slightly better for rough covariance kernels.
