Date of Award
2018
Document Type
Open Access Master's Thesis
Degree Name
Master of Science in Mathematical Sciences (MS)
Administrative Home Department
Department of Mathematical Sciences
Advisor 1
Allan A. Struthers
Committee Member 1
Benjamin W. Ong
Committee Member 2
Cecile M. Piret
Abstract
Roots of a scalar polynomial in one variable are frequently found by computing the eigenvalues of the standard companion matrix. In this exploratory work, we introduce the pseudo-companion matrix for finding roots of multivariable polynomial systems. In some cases, a perturbation of the polynomial system is used for the matrix construction, yielding approximate roots of the original polynomial system. The coordinates of the roots, or their approximations, are obtained from the eigenvectors of this matrix. In this thesis, we describe the process of constructing the pseudo-companion matrix and computing the polynomial roots using illustrative examples.
Recommended Citation
Kleczynski, Melinda, "Pseudo-Companion Matrices for Polynomial Systems", Open Access Master's Thesis, Michigan Technological University, 2018.