Optimal recovery by linear functions (Q1063187)

In optimal recovery one has linear information on a function f, satisfying an additional side condition. The information may also be disturbed by an error \(\epsilon\). One wishes to recover a value Uf that is linear dependent on f, minimizing the worst case error. The paper proves that there is a linear optimal recovery algorithm if the side condition on f defines a convex and balanced set and U is a linear mapping to \({\mathbb{R}}\). Also conditions for the existence of a linear and continuous optimal algorithm and its uniqueness are given.