How powerful is continuous nonlinear information for linear problems?
The paper discusses the question, how much information one can deduce about the best approximation of a solution to a problem which depends on an unknown function f, of which only partial information N(f) is known; here N is an operator defined on a given class of functions with values in \({\mathbb{R}}^ n\); cf. the book by \textit{J. F. Traub}, the second author and \textit{H. Wózniakowski} [Information, uncertainty, complexity. (1983; Zbl 0522.68041)]. While many results are known for linear information operators, this paper discusses the nonlinear, but continuous, case. It is shown that for worst case behaviour, nonlinear information gives no less uncertainty than suitable linear information, while on the average, the uncertainty can be considerably reduced.
scientific article; zbMATH DE number 4003378