June 2020
Intermediate to advanced
158 pages
4h 36m
English
Content preview from Multivariate Algorithms and Information-Based Complexity
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6 ε-Superposition and truncation dimensions, and multivariate method for ∞-variate linear problems
G. W. Wasilkowski
Computer Science Department, University of Kentucky, Lexington, USA
Abstract
The paper deals with linear problems defined on -weighted normed spaces of functions with infinitely many variables. In particular, we present results on ε-truncation and ε-superposition dimensions, which show conditions under which these dimensions are small under modest error demand ε. We also discuss multivariate decomposition methods and their effectiveness in reducing infinitely many variables to a relatively small number equal to the ε-superposition dimension. These positive results are derived for the so called anchored decomposition. In ...
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