Abstract
A new numerical method for solving Fredholm integral equations of the third kind over finite intervals is presented. The integral operator is represented by a square matrix which is computed by means of a two-dimensional series expansion of the kernel function with respect to a complete orthonormal set. The method is especially useful in computing the Karhunen-Loèvo expansion of a stochastic process and the best approximation of a function of two variables by a sum of products of functions of a single variable. Here the Karhunen-Loève expansion of a well-known stochastic process is considered. These techniques can be applied to deterministic and stochastic control systems.
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