Modifying a Sparse Cholesky Factorization

@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
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