On adaptive information with varying cardinality for linear problems with elliptically contoured measures

Abstract

Adaptive information is not more powerful than nonadaptive information for solving linear problems with elliptically contoured measures provided that the cardinality of information is fixed (see G. W. Wasilkowski and H. Woźniakowski, 1984, Numer. Math.44, 169–190). Can adaptive information be essentially more powerful than nonadaptive information when cardinality is allowed to vary? The answer is negative if a Gaussian measure is considered (see G. W. Wasilkowski, 1986, J. Complexity2, 204–228). This work generalizes the result to a class of elliptically contoured measures for which the answer is still negative.