Matroid Filtrations and Computational Persistent Homology

This technical report introduces a novel approach to efficient computation in
homological algebra over fields, with particular emphasis on computing the
persistent homology of a filtered topological cell complex. The algorithms here
presented rely on a novel relationship between discrete Morse theory, matroid
theory, and classical matrix factorizations. We provide background, detail the
algorithms, and benchmark the software implementation in the Eirene package.