Dodgson's determinant: a qualitative analysis

Abstract

Condensation, developed by Charles Dodgson, is an uncommon method for calculating the determinant of a matrix. It is generally considered to be numerically unstable due to its iterative nature. While we do not attempt to prove whether or not the algorithm is stable, we conduct a qualitative stability analysis. We compare the algorithm's performance to that of row reduction on contrived and random matrices. We test two modified condensation algorithms for 3#2;3 and 4#2;4 matrices, which we include in our comparisons as well. We also briefly investigate the relationship between the condition number of a matrix and the performance of these algorithms when used to calculate its determinant.