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Dissertation/Thesis Abstract

Pseudo-companion Matrices for Polynomial Systems
by Kleczynski, Melinda, M.S., Michigan Technological University, 2018, 113; 10791562
Abstract (Summary)

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.

Indexing (document details)
Advisor: Struthers, Allan A.
Commitee: Ong, Benjamin W., Piret, Cecile M.
School: Michigan Technological University
Department: Mathematical Sciences
School Location: United States -- Michigan
Source: MAI 57/06M(E), Masters Abstracts International
Subjects: Applied Mathematics
Keywords: Companion matrix, Numerical algebraic geometry, Numerical polynomial algebra, Polynomial system solving
Publication Number: 10791562
ISBN: 978-0-355-97958-9
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