Sparse Exact Factorization Update

To meet the growing need for extended or exact precision solvers, an efficient framework based on Integer-Preserving Gaussian Elimination (IPGE) has been recently developed which includes dense/sparse LU/Cholesky factorizations and dense LU/Cholesky factorization updates for column and/or row replacement. In this paper, we discuss our on-going work developing the sparse LU/Cholesky column/row-replacement update and the sparse rank-l update/downdate. We first present some basic background for the exact factorization framework based on IPGE. Then we give our proposed algorithms along with some implementation and data-structure details. Finally, we provide some experimental results showcasing the performance of our update algorithms. Specifically, we show that updating these exact factorizations can be typically 10x to 100x faster than (re-)factorizing the matrices from scratch.