Fraction-Free Methods for Determinants

<p>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.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2011

Author dc:creator

• Leggett, Deanna Richelle

Contributors dc:contributor

• John Perry

• Mathematics

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/1

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1001