Date of Award
Spring 5-2011
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
Committee Chair
John Perry
Committee Chair Department
Mathematics
Abstract
Given a matrix of integers, we wish to compute the determinant using a method that does not introduce fractions. Fraction-Free Triangularization, Bareiss’ Algorithm (based on Sylvester’s Identity) and Dodgson’s Method (based on Jacobi’s Theorem) are three such methods. However, both Bareiss’ Algorithm and Dodgson’s Method encounter division by zero for some matrices. Although there is a well-known workaround for the Bareiss Algorithm that works for all matrices, the workarounds that have been developed for Dodgson’s method are somewhat difficult to apply and still fail to resolve the problem completely. After investigating new workarounds for Dodgson’s Method, we give a modified version of the old method that relies on a well-known property of determinants to allow us to compute the determinant of any integer matrix.
Copyright
2011, Deanna Richelle Leggett
Recommended Citation
Leggett, Deanna Richelle, "Fraction-Free Methods for Determinants" (2011). Master's Theses. 1.
https://aquila.usm.edu/masters_theses/1