Abstract
We study the asymptotic behavior of the minimal cost of computing an ϵ-approximation to linear continuous operators, as ϵ → 0+. An approximation is computed based on perturbed values of linear and continuous functionals which can be chosen adaptively. Obtaining a value of a functional with given precision is connected with some cost determined by the cost function. Under some assumptions, we show that the minimal (information) cost of computing an ϵ-approximation grows essentially as fast as the minimal information cost in the worst case setting. It can grow significantly slower only on a boundary set of problem elements. A nonadaptive method with the information cost proportional to the minimal worst case cost is constructed.
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