EFFICIENT WAVELET TRANSFORM OF COVARIANCE FUNCTIONS USING MALLAT’S TREE ALGORITHM FOR K-L SIMULATION

Abstract eng:
The feasibility of implementing K-L expansion as a practical simulation tool hinges crucially on the ability to compute a large number of K-L terms accurately and cheaply. This paper demonstrates that a discrete wavelet transform scheme based on the Mallat’s tree algorithm can be exploited to solve the Fredholm integral equation efficiently for practical K-L simulation. The rate of convergence and CPU time needed to obtain eigensolutions for the exponential and squared exponential covariance functions using Harr wavelets, trigonometrics and Legendre polynomials are discussed.

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