Information of varying cardinality
We study adaptive information of varying cardinality for linear problems defined on a separable Banach space. It is known that for linear problems adaptive information of fixed cardinality does not help in the worst case setting. It does not help also in the average case setting with Gaussian measures. We prove that in the worst case setting a similar result holds for information of varying cardinality. In the average case setting with Gaussian measures, information of varying cardinality can be more powerful than information of fixed cardinality. However, optimal information has a structure which is almost as simple as nonadaptive information of fixed cardinality. We also give a condition under which varying cardinality does not help. These results are useful for deriving tight bounds on complexity, which is also studied in this paper.
adaptive information of varying cardinality
linear problems defined on a separable Banach space
scientific article; zbMATH DE number 3997695
scientific article