A Note About Algebraic $(s,t)$-Weak Tractability Of Linear Tensor Product Problems In The Worst-Case Setting

Abstract

This paper is devoted to discussing the linear tensor product problems in the worst case setting. We consider algorithms that use finitely many evaluations of arbitrary continuous linear functionals. We investigate algebraic $(s,t)$-weak tractability (ALG-$(s,t)$-WT) under the absolute error criterion in the case $\hat{I}{»}_1>1$, where $\hat{I}{»}_1$ is the square of the univariate maximal singular value. We solve the problem by giving the necessary and sufficient conditions for ALG-$(s,t)$-WT on univariate singular values and fill the gap left open.

11 pages