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Ε-Superposition And Truncation Dimensions In Average And Probabilistic Settings For ∞-Variate Linear Problems, Jonathan M. Dingess

Theses and Dissertations--Computer Science

This thesis is a representation of my contribution to the paper of the same name I co-author with Dr. Wasilkowski. It deals with linear problems defined on γ-weighted normed spaces of functions with infinitely many variables. In particular, I describe methods and discuss results for ε-truncation and ε-superposition methods. I show through these results that the ε-truncation and ε-superposition dimensions are small under modest error demand ε. These positive results are derived for product weights and the so-called anchored decomposition.