# U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology

@article{Hang2021UmatchFS, title={U-match factorization: sparse homological algebra, lazy cycle representatives, and dualities in persistent (co)homology}, author={Haibin Hang and Chad Giusti and Lori Ziegelmeier and Gregory Henselman-Petrusek}, journal={ArXiv}, year={2021}, volume={abs/2108.08831} }

Persistent homology is a leading tool in topological data analysis (TDA). Many problems in TDA can be solved via homological – and indeed, linear – algebra. However, matrices in this domain are typically large, with rows and columns numbered in billions. Low-rank approximation of such arrays typically destroys essential information; thus, new mathematical and computational paradigms are needed for very large, sparse matrices. We present the U-match matrix factorization scheme to address this…

## One Citation

### The space of barcode bases for persistence modules

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A new algorithm for computing barcodes which also keeps track of, and outputs, such a change of basis and an explicit characterisation of the group of transformations that sends one barcode basis to another.

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