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Table 2 Numerical complexity of the standard KLE and the conditioned KLE

From: Large scale random fields generation using localized Karhunen–Loève expansion

Operation Standard KLE Conditioned KLE
Kernel modal decomposition \(\mathcal {O}((n_sM)^{3d})\) \(\mathcal {O}(n_s^{3d})\)
Conditioning matrices computation \(\mathcal {O}(N^3(3^d-1)^3)\)
Random field sampling \(\mathcal {O}(n_s^d M^{2d} N)\) \(\mathcal {O}((n_sM)^dN)\)
  1. Non-tensorizable covariance kernel. \(n_s\) number of discretization steps of a segment of length L, M number of prolongations in one direction, d dimension, N total number of retained KLE terms for \(M=1\)