STaRS: Yugendra Uppalapati (TAMS) | Department of Mathematics

STaRS: Yugendra Uppalapati (TAMS)

Event Information
Event Location: 
GAB 461
Event Date: 
Friday, October 14, 2022 - 2:00pm

Mentors: Joseph Prein (UNT Graduate) and Dr. Nam Trang

Title: Investigating Exact Cancellations in Cholesky Decompositions Via Schur's Complements and Graphs

Abstract: This research project investigates solving systems of equations of the form Ax = b and its applications, where A is a sparse symmetric positive definite matrix, by considering the Cholesky factorization of A via graph-theoretic techniques, such as constructing fill graphs. The primary goal is to show whether or not there always exists permutations of a symmetric positive definite matrix with no exact cancellations in the fill graph. It has been shown so far that such permutations exist for the 3x3, 4x4, & the 5x5 matrices by focusing on specific subcases and showing that each subcase can be permuted so that there are no exact cancellations that aren't later filled-in after taking all the Schur's complements. The general nxn case is currently being investigated.

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