Date of Award
2024
Document Type
Open Access Master's Report
Degree Name
Master of Science in Mathematical Sciences (MS)
Administrative Home Department
Department of Mathematical Sciences
Advisor 1
Jiguang Sun
Committee Member 1
Allan Struthers
Committee Member 2
Zhengfu Xu
Abstract
The condition number, being critical to solving linear systems, has many impor-
tant applications. Specifically for robust control analysis, the Euclidean norm has
widespread use over the 1-norm and ∞-norm such as determining a control system’s
stability to uncertainty [1]. Much work has been done with estimating the Euclidean
condition number, but current algorithms for computing said condition number, with
large matrices, tend to run slow as well as requiring a large amount of computa-
tional resources. This report seeks to provide a more time efficient algorithm that
utilizes MATLAB’s eigs, svds, and normest commands as well as the recently devel-
oped RIM-C that can be ran with off-the-shelf software with commercially available
hardware.
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 4.0 License.
Recommended Citation
McCarthy, Cody, "NEW METHOD FOR COMPUTING THE EUCLIDEAN CONDITION NUMBER WITH RIM-C", Open Access Master's Report, Michigan Technological University, 2024.