Optimal average case estimation in Hilbert norms (Q1841267)

Two local average case error measures of algorithms are considered. They are based on noisy information and on Hilbert norms, as well as information spaces. The optimal algorithm is defined. Formulas for its two local errors are provided. They explicitly exhibit the influence of factors such as information, information errors, norms in the considered spaces, etc. Based on the error expression, the problem of selecting the optimal approximating space is formulated. The solution is given with a specific formula for the error depending on the equivalence of a certain matrix defined by information and norms.