Date of Award
Master of Science (MS)
In this work, we study contractive and positive real matrix completion problems which are motivated in part by studies on sparce (or dense) matrices for weighted sparse recovery problems and rating matrices with rating density in recommender systems. Matrix completions problems also have many applications in probability and statistics, chemistry, numerical analysis (e.g. optimization), electrical engineering, and geophysics. In this paper we seek to connect the contractive and positive completion property to a graph theoretic property. We then answer whether the graphs of real symmetric matrices having loops at every vertex have the contractive completion property if and only if the graph of said matrix is chordal. If this is not true, we characterize all graphs of real symmetric matrices having the contractive completion property.
Christopher, Louis C., "Matrix Completion Problems for the Positiveness and Contraction Through Graphs" (2023). Theses and Dissertations - UTRGV. 1329.