Multiple-rank modifications of a sparse Cholesky factorization

Given a sparse symmetric positive definite matrix AA(T) and an associated s parse Cholesky factorization LDLT or LLT, we develop sparse techniques for updating the factorization after either adding a collection of columns to A or deleting a collection of columns from A. Our techniques are based on an analysis and manipulation of the underlying graph structure, using the fra mework developed in an earlier paper on rank-1 modi cations [ T. A. Davis a nd W. W. Hager, SIAM J. Matrix Anal. Appl., 20 (1999), pp. 606-627]. Comput ationally, the multiple-rank update has better memory traffic and executes much faster than an equivalent series of rank-1 updates since the multiple- rank update makes one pass through L computing the new entries, while a ser ies of rank-1 updates requires multiple passes through L.