CISE Submissions

Item: REP-1997-261

Item:REP-1997-261

Title:Modifying a Sparse Cholesky Factorization (revision of TR-97-003)

Timothy A. Davis
William W. Hager

Abstract:
Given a sparse symmetric positive definite matrix AA' and an associated sparse Cholesky factorization LDL' or LL', 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, Golub, Murray, and Saunders for modifying a dense Cholesky factorization. We show that our methods extend to the general case where an arbitrary sparse symmetric positive definite matrix is modified. Our methods are optimal in the sense that they take time proportional to the number of nonzero entries in L and D that change.

Supporting File:here

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