Notes on tractability conditions for linear multivariate problems
Provides theoretical foundations for understanding tractability in multivariate approximation problems, relevant to researchers in numerical analysis and approximation theory.
The paper establishes necessary and sufficient conditions for tractability of compact linear multivariate operators over Hilbert spaces, expressed in terms of sums of functions of singular values without requiring their ordering.
We study approximations of compact linear multivariate operators defined over Hilbert spaces. We provide necessary and sufficient conditions on various notions of tractability. These conditions are mainly given in terms of sums of certain functions depending on the singular values of the multivariate problem. They do not require the ordering of these singular values which in many cases is difficult to achieve.