Correction to: Fast random field generation with H-matrices

1 Correction to: Numer. Math. (2018) 140:639–676 https://doi.org/10.1007/s00211-018-0974-2

On page 3 in line -4, the correct statement is

… μ ∈ (0, ∞], p ∈ 2ℕ are parameters.

The corrected version states the parameter range as p ∈ 2ℕ instead of p ∈ ℕ. The effect is to disallow non-smooth norms such as the ℓ₁-norm for the distance measure. This, however, does not impact the usual definition of the Matérn class of covariance functions using the ℓ₂-norm for all values of μ ∈ (0, ∞] (particularly the exponential case for μ = 1/2 and the Gaussian case for μ = ∞). Moreover, all the numerical examples and particularly the non-stationary covariance functions on page 642 are still covered by the theory.

This minor change closes the small gap in the proof of Lemma 1 by ensuring the existence of all the derivatives which are shown to be bounded in the sense of asymptotic smoothness (1).