Fig. 1. Relative eigenvalue errors from simulation using wavelet-based K–L expansion with M=N: (a) 10,000 realisations and (b) 100,000 realisations (closed symbol: simulation, open symbol: theory).

Fig. 2. Relative eigenvalue errors from simulation (after orthogonalization) using wavelet-based K–L expansion with M=N for 10,000 realisations (closed symbol: simulation, open symbol: theory).

Fig. 3. Eigenvalues of exponential covariance function evaluated using N=512 wavelet basis functions for various normalized length of the process (a/b).

Table 1. Statistical correlations in the simulation of standard Gaussian variates ξ_k(θ) using pseudo-random number generator ran1 with Box–Muller transform

Note: r_max=maximum off-diagonal entry in correlation matrix R, r_crit=critical value for rejecting null hypothesis of zero correlation at 5% level of significance.

Table 2. Comparison of runtime (s) required for simulating 10,000 realisations using K–L expansion (Eq. (15)) and Cholesky expansion (Eq. (17)) with M=N

Table 3. Comparison of runtime (s) for generating different normalized length of processes using the truncated K–L expansion with MN, K–L expansion with M=N and Cholesky expansion with M=N (N=512 for all cases)