Different covariance kernels are defined to illustrate three series expansion methods for 1D random field representation: (i) the 'expansion optimal linear estimator (EOLE)', (ii) the orthogonal series expansion (OSE)', and (iii) the 'Karhunen-Loève (K-L)' methods. The solution of the K-L eigenvalue problem is computed with the Discrete, Nyström and Galerkin methods. The main references are: "Stochastic finite element methods and reliability" by Sudret and Der Kiureghian, and "Stochastic finite elements: a spectral approach" by Ghanem and Spanos.
Several references to equations and useful comments are written in order to provide a better understanding of the codes. The programs estimate the corresponding eigenvalues and eigenvectors of the covariance kernel, and plot several random field realizations, together with the covariance approximation.
Any suggestions, corrections and/or improvements are kindly accepted :-)
Felipe Uribe (2022). Random field representation methods (https://www.mathworks.com/matlabcentral/fileexchange/52372-random-field-representation-methods), MATLAB Central File Exchange. Recuperado .
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