Abstract
In LAPACK there are two types of subroutines for solving problems with symmetric matrices: routines for full and packed storage. The performance of full format is much better as it allows the usage of Level 2 and 3 BLAS whereas the memory requirement of the packed format is about 50% of full. We propose a new storage layout which combines the advantages of both algorithms: its factorization performance is better than that of full storage layout, and its memory requirement is percentage-wise slightly larger than packed storage.
Our new algorithms, called DBSSV, DBSTRF, and DBSTRS are now part of ESSL[9]. On three recent IBM RS/6000 platforms, Power3, Power2 and PowerPC 604e DBSTRF outperforms LAPACK’s DSYTRF by about 20%, and DBSTRS, with 100 RHS, outperforms LAPACK’s DSYTRS by more than 100%. These performance results are decidedly unfair to our new algorithms: we compare against Level 3 algorithms as opposed to Level 2 packed algorithms.
This research is supported by the UNI•C collaboration with the IBM T.J. Watson Research Center at Yorktown Heights. The research of the last author was supported by Grants MM-707 and I-702 of the Bulgarian Ministry of Education and Science.
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References
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Gustavson, F., Karaivanov, A., Marinova, M., Waśniewski, J., Yalamov, P. (2001). A Fast Minimal Storage Symmetric Indefinite Solver. In: Sørevik, T., Manne, F., Gebremedhin, A.H., Moe, R. (eds) Applied Parallel Computing. New Paradigms for HPC in Industry and Academia. PARA 2000. Lecture Notes in Computer Science, vol 1947. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-70734-4_14
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DOI: https://doi.org/10.1007/3-540-70734-4_14
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