The worst case complexity of the fredholm equation with periodic free term and noisy information

This paper deals with the complexity of the Fredholm equation La = f of the second kind with f is an element of H'(Gamma) in a periodic setting. The problem elements are free term f and belong to the unit ball of H'(Gamma). Available information about the problem element f is assumed to be corrupted by bounded noise. First, we give the order of the n-the optimal radius in the worst case setting. Then, we show that the Galerkin method using 2n + 1 inner products off has minimal error. Finally, we give the estimate of E-complexity of the Fredholm integral equation of the second kind and the Galerkin method in the worst case setting.

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