Tractability Of Approximation In Korobov Space In The Average Case Setting Based On Standard Information

The tractability problems of general linear problems in the average case setting are studied.By using the algorithms constructed by finite evaluations of continuous linear functionals,we discussed the relationship of the optimal convergence rate and the tractability,the necessary and sufficient conditions for tractability of general multivariate linear problems are obtained.Specifically,we studied the multivariate approximation problems with respect to a zero-mean Gaussian measure.For the normalized error criterion,the necessary and sufficient conditions are obtained for the approximation problem of a kind of Korobov spaces being tractable in some sense.The results are terms of its weight sequence.