Factoring Symmetric Indefinite Matrices on High-Performance Architectures

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Abstract
The Bunch–Kaufman algorithm is the method of choice for factoring symmetric indefinite matrices in many applications. However, the Bunch–Kaufman algorithm uses matrix-vector operations and, therefore, may not take full advantage of high-performance architectures with a memory hierarchy. It is possible to modify the Bunch–Kaufman algorithm so that it uses rank-k updates. However, this straightforward modification allows unrestricted row/column interchanges during the algorithm, thus making it unsuitable for banded and sparse matrix factorization. A new algorithm, based on Bunch–Kaufman factorization, is described that uses rank-k updates to take advantage of high-performance architectures while limiting the number of row/column interchanges. Results from implementations on the CRAY Y-MP and the Alliant FX/8 are presented.

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