Date of Award
Honors College Thesis
A computer can use a matrix to represent a system of non-linear multivariate polynomial equations. The fastest known ways to transform this system into a form with desirable computational properties rely on transforming its matrix into upper-triangular form [8, 9]. The matrix for such a system will have mostly zero entries, which we call sparse . We propose to analyze several methods of performing row-reduction, the process by which matrices are reduced into upper-triangular form .
What is special about row-reducing matrices in this context? When row-reducing a matrix, swapping rows or columns is typically acceptable. However, if the order of the terms in the polynomials must be preserved as in nonlinear systems, swapping columns of its matrix would be unacceptable. Another thing to consider is the “almost” upper-triangular structure of these matrices. Therefore, we want to adapt methods of performing row-reduction to allow swapping rows but not columns and perform the least amount of additions and multiplications.
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Debenport, Lorrin, "Row Reduction of Macaulay Matrices" (2011). Honors Theses. 184.