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.
|Advisor:||Struthers, Allan A.|
|Commitee:||Ong, Benjamin W., Piret, Cecile M.|
|School:||Michigan Technological University|
|School Location:||United States -- Michigan|
|Source:||MAI 57/06M(E), Masters Abstracts International|
|Keywords:||Companion matrix, Numerical algebraic geometry, Numerical polynomial algebra, Polynomial system solving|
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