Matrix computations (3rd ed.)
Recursion leads to automatic variable blocking for dense linear-algebra algorithms
IBM Journal of Research and Development
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Recursive Blocked Data Formats and BLAS's for Dense Linear Algebra Algorithms
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
Applying recursion to serial and parallel QR factorization leads to better performance
IBM Journal of Research and Development
LAWRA: Linear Algebra with Recursive Algorithms
PARA '00 Proceedings of the 5th International Workshop on Applied Parallel Computing, New Paradigms for HPC in Industry and Academia
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
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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, Po- wer2 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.