The Worst Case Complexity of the Fredholm Equation of the Second Kind with Non-Periodic Free Term and Noise Information
نویسنده
چکیده
This paper deals with the complexity of the Fredholm equation Lu = f of the second kind with f 2 W r;p ((). The problem elements are free term f and belong to the unit ball of W r;p ((). Available information about the problem consists of evaluations of f and is assumed to be corrupted by uniformly bounded noise. The absolute error in each noisy evaluation is at most. First, we give estimation of the n-th optimal radius in the worst case setting. Then, we show that a noisy nite element method with quadrature (FEMQ) has minimal error. Finally, we give the estimate of "-complexity of Fredholm problem of the second kind in the worst case setting. To the best of our knowledge, this is the rst work on complexity of integral equation with noisy information.
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