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A Note on the Column Elimination Tree

John R. Gilbert Laura Grigori 1
1 RESEDAS - Software Tools for Telecommunications and Distributed Systems
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : 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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Submitted on : Friday, May 19, 2006 - 6:35:37 PM
Last modification on : Friday, February 4, 2022 - 3:34:44 AM
Long-term archiving on: : Saturday, April 3, 2010 - 11:26:01 PM


  • 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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