Yan, H.; Chen, J. Exponential Convergence-(t,s)-Weak Tractability of Approximation in Weighted Hilbert Spaces. Mathematics2024, 12, 2067.
Yan, H.; Chen, J. Exponential Convergence-(t,s)-Weak Tractability of Approximation in Weighted Hilbert Spaces. Mathematics 2024, 12, 2067.
Yan, H.; Chen, J. Exponential Convergence-(t,s)-Weak Tractability of Approximation in Weighted Hilbert Spaces. Mathematics2024, 12, 2067.
Yan, H.; Chen, J. Exponential Convergence-(t,s)-Weak Tractability of Approximation in Weighted Hilbert Spaces. Mathematics 2024, 12, 2067.
Abstract
We study L_2-approximation problems in the weighted Hilbert spaces in the worst case setting. Three interesting weighted Hilbert spaces appear in this paper, whose weights are equipped with two positive parameters $\ga_j$ and $\az_j$ for $j=1,\,2,\dots,\,d$. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. We discuss the exponential convergence-(t,s)-weak tractability (EC-(t,s)-WT) of these L_2-approximation problems under the absolute or normalized error criterion. In particular, we obtain the sufficient and necessary conditions for EC-(1,1)-WT and EC-(t,1)-WT with t
Keywords
L_2-approximation; information complexity; tractability; weighted Hilbert spaces
Subject
Computer Science and Mathematics, Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
