EC-(s,t)-Weak Tractability Of Multivariate Linear Problems In The Average Case Setting

This study aimed to investigate EC-(s,t)-weak tractability of multivariate linear problems in the average case setting.The consider algorithms use finitely many evaluations of arbitrary linear functionals.Generally,we obtained the matching necessary and sufficient conditions for EC-(s,t)-weak tractability in terms of the corresponding non-increasing eigenvalue sequence.Specifically,we discussed EC-(s.t)-weak tractability of linear tensor product problems and obtained the necessary and sufficient conditions in terms of the corresponding one-dimensional problem.As an example,we discussed the EC-(s,t)-weak tractability of a multivariate Korobov approximation problems.