The design and implementation of a new out-of-core sparse cholesky factorization method

Vladimir Rotkin, Sivan Toledo

Research output: Contribution to journalArticlepeer-review

Abstract

We describe a new out-of-core sparse Cholesky factorization method. The new method uses the elimination tree to partition the matrix, an advanced subtree-scheduling algorithm, and both right-looking and left-looking updates. The implementation of the new method is efficient and robust. On a 2 GHz personal computer with 768 MB of main memory, the code can easily factor matrices with factors of up to 48 GB, usually at rates above 1 Gflop/s. For example, the code can factor AUDIKW, currenly the largest matrix in any matrix collection (factor size over 10 GB), in a little over an hour, and can factor a matrix whose graph is a 140-by-140-by-140 mesh in about 12 hours (factor size around 27 GB).

Original languageEnglish
Pages (from-to)19-46
Number of pages28
JournalACM Transactions on Mathematical Software
Volume30
Issue number1
DOIs
StatePublished - Mar 2004

Keywords

  • Out-of-core

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