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Reports (Technical Report) Year : 2001

A Note on the Column Elimination Tree


This short communication considers the LU factorization with partial pivoting and shows that an all-at-once result is possible for the structure prediction of the column dependencies in L and U. Specifically, we prove that for every square strong Hall matrix A there exists a permutation P such that every edge of its column elimination tree corresponds to a symbolic nonzero in the upper triangular factor U. In the symbolic sense, this resolves a conjecture of Gilbert and Ng [6].
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inria-00069923 , version 1 (19-05-2006)


  • HAL Id : inria-00069923 , version 1


John R. Gilbert, Laura Grigori. A Note on the Column Elimination Tree. [Technical Report] RT-0251, INRIA. 2001, pp.7. ⟨inria-00069923⟩
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