@article{Davis1999ModifyingAS,
title={Modifying a Sparse Cholesky Factorization},
author={Timothy A. Davis and William W. Hager},
journal={SIAM J. Matrix Analysis Applications},
year={1999},
volume={20},
pages={606-627}
}

Given a sparse symmetric positive definite matrix AAT and an associated sparse Cholesky factorization LDLT or LLT, we develop sparse techniques for obtaining the new factorization associated with either adding a column to A or deleting a column from A. Our techniques are based on an analysis and manipulation of the underlying graph structure and on ideas of Gill et al. [Math. Comp., 28 (1974), pp. 505–535] for modifying a dense Cholesky factorization. We show that our methods extend to the… CONTINUE READING