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

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

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...

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Bibliographic Details
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
Description
Summary: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.

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