Tractability of Approximation of Functions Defined over Weighted Hilbert Spaces

• DOI: 10.20944/preprints202312.2272.v1
• Publication Date: 2024-01-03T00:54:56Z
• Authors: Huichao Yan; Jia Chen
• Keywords: multivariate approximation; tractability; QA1-939; information complexity; 0101 mathematics; weighted Hilbert spaces; Mathematics

We investigate \texorpdfstring{$L_2$}{}-approximation problems in the worst case setting weighted Hilbert spaces \texorpdfstring{$H(K_{R_{d,\a,\g}})$}{} with weights \texorpdfstring{$R_{d,\a,{\bm \ga}}$}{} under parameters \texorpdfstring{$1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$ and $1<\az_1\le \az_2\le \cdots$}{}. Several interesting appear this paper. consider error of algorithms that use finitely many arbitrary continuous linear functionals. Multivariate approximation; information complexity; tractability; spacesWe discuss tractability for involved spaces, which describes how complexity depends on \texorpdfstring{$d$}{} \texorpdfstring{$\va^{-1}$}{}. As a consequence we study strongly polynomial (SPT), (PT), weak (WT), \texorpdfstring{$(t_1,t_2)$}{}-weak (\texorpdfstring{$(t_1,t_2)$}{}-WT) all \texorpdfstring{$t_1>1$}{} \texorpdfstring{$t_2>0$}{} terms introduced absolute criterion or normalized criterion.