ε-SUPERPOSITION AND TRUNCATION DIMENSIONS IN AVERAGE AND PROBABILISTIC SETTINGS FOR ∞-VARIATE LINEAR PROBLEMS

• Main Author: Dingess, Jonathan M.
• Format: Others
• Published: UKnowledge 2019
• Subjects: infinite-variate linear problems; epsilon-superposition; epsilon-truncation; product weights; multivariate decomposition methods; changing dimension algorithms; Computer Sciences; Mathematics
• Online Access: https://uknowledge.uky.edu/cs_etds/81; https://uknowledge.uky.edu/cgi/viewcontent.cgi?article=1084&context=cs_etds

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.