## HPL References

**The list of references below contains some relevant published material to this work. This list is provided for illustrative purposes, and should be regarded as an initial starting point for the interested reader. This list is by all means not meant to be exhaustive.**

The references have been sorted in four categories and chronologically listed within each category. The four categories are

- Linpack Benchmark
- Parallel LU Factorization
- Recursive LU Factorization
- Parallel Matrix Multiply
- Parallel Triangular Solve

### Linpack Benchmark

*LINPACK Users Guide*, J. Dongarra, J. Bunch, C. Moler and G. W. Stewart, SIAM, Philadelphia, PA, 1979.*Performance of Various Computers Using Standard Linear Equations Software*, J. Dongarra, Technical Report CS-89-85, University of Tennessee, 1989. (An updated version of this report can be found at http://www.netlib.org/benchmark/performance.ps).*Towards Peak Parallel LINPACK Performance on 400*, R. Bisseling and L. Loyens, Supercomputer, Vol. 45, pp. 20-27, 1991.*Massively Parallel LINPACK Benchmark on the Intel Touchstone DELTA and iPSC/860 Systems*, R. van de Geijn, 1991 Annual Users Conference Proceedings. Intel Supercomputer Users Group, Dallas, TX, 1991.*The LINPACK Benchmark on the AP 1000*, R. Brent, Frontiers, 1992, pp. 128-135, McLean, VA, 1992.*Implementation of BLAS Level 3 and LINPACK Benchmark on the AP1000*, R. Brent and P. Strazdins, Fujitsu Scientific and Technical Journal, Vol. 5, No. 1, pp. 61-70, 1993.*LU Factorization and the LINPACK Benchmark on the Intel Paragon*, D. Womble, D. Greenberg, D. Wheat and S. Riesen, Sandia Technical Report, 1994.*Massively Parallel Distributed Computing: Worlds First 281 Gigaflop Supercomputer*, J. Bolen, A. Davis, B. Dazey, S. Gupta, G. Henry, D. Robboy, G. Schiffler, D. Scott, M. Stallcup, A. Taraghi, S. Wheat from Intel SSD, L. Fisk, G. Istrail, C. Jong, R. Riesen, L. Shuler, from Sandia National Laboratories, Proceedings of the Intel Supercomputer Users Group 1995.*High Performance Software on Intel Pentium Pro Processors or Micro-Ops to TeraFLOPS*, B. Greer and G. Henry, Proceedings of the SuperComputing 1997 Conference, ACM SIGARCH - IEEE Computer Society Press - ISBN: 0-89791-985-8, San Jose, CA, 1997.

### Parallel LU Factorization

*Communication Complexity of the Gaussian Elimination Algorithm on Multiprocessors*, Y. Saad, Linear Algebra and Its Applications, Vol. 77, pp. 315-340, 1986.*LU Factorization Algorithms on Distributed-Memory Multiprocessor Architectures*, G. Geist and C. Romine, SIAM Journal on Scientific and Statistical Computing, Vol. 9, pp. 639-649, 1988.*Parallel LU Decomposition on a Transputer Network*, R. Bisseling and J. van der Vorst, Lecture Notes in Computer Sciences, Springer-Verlag, Eds. G. van Zee and J. van der Vorst, Vol. 384, pp. 61-77, 1989.*The Distributed Solution of Linear Systems Using the Torus-Wrap Data Mapping*, C. Ashcraft, ECA-TR-147, Boeing Computer Services, Seattle, WA, 1990.*Experiments with Multicomputer LU-Decomposition*, E. van de Velde, Concurrency: Practice and Experience, Vol. 2, pp. 1-26, 1990.*A Taxonomy of Distributed Dense LU Factorization Methods*, C. Ashcraft, ECA-TR-161, Boeing Computer Services, Seattle, WA, 1991.*The Torus-Wrap Mapping for Dense Matrix Calculations on Massively Parallel Computers*, B. Hendrickson and D. Womble, SIAM Journal on Scientific and Statistical Computing, Vol. 15, pp. 1201-1226, 1994.*Scalability Issues in the Design of a Library for Dense Linear Algebra*, J. Dongarra, R. van de Geijn and D. Walker, Journal of Parallel and Distributed Computing, Vol. 22, No. 3, pp. 523-537, 1994.*Matrix Factorization using Distributed Panels on the Fujitsu AP1000*, P. Strazdins, Proceedings of the IEEE First International Conference on Algorithms And Architectures for Parallel Processing ICA3PP-95, Brisbane, 1995.*The Design and Implementation of the ScaLAPACK LU, QR, and Cholesky Factorization Routines*, J. Choi, J. Dongarra, S. Ostrouchov, A. Petitet, D. Walker and R. C. Whaley, Scientific Programming, Vol. 5, pp. 173-184, 1996.

### Recursive LU Factorization

*Locality of Reference in LU Decomposition with partial pivoting*, S. Toledo, SIAM Journal on Matrix. Anal. Appl., Vol. 18, No. 4, 1997.*Recursion Leads to Automatic Variable Blocking for Dense Linear-Algebra Algorithms*, F. Gustavson, IBM Journal of Research and Development, Vol. 41, No. 6, pp. 737-755, 1997

### Parallel Matrix Multiply

*Matrix Algorithms on a Hypercube I: Matrix Multiplication*, G. Fox, S. Otto and A. Hey, Parallel Computing, Vol. 3, pp. 17-31, 1987.*Basic Matrix Subprograms for Distributed-Memory Systems*, A. Elster, Proceedings of the Fifth Distributed-Memory Computing Conference, Eds. D. Walker and Q. Stout, IEEE Press, pp. 311-316, 1990.*The Parallelization of Level 2 and 3 BLAS Operations on Distributed-Memory Machines*, M. Aboelaze, N. Chrisochoides and E. Houstis, CSD-TR-91-007, Purdue University, West Lafayette, IN, 1991.*The Multicomputer Toolbox Approach to Concurrent BLAS and LACS*, R. Falgout, A. Skjellum, S. Smith and C. Still, Proceedings of the Scalable High Performance Computing Conference SHPCC-92, IEEE Computer Society Press, 1992.*A High Performance Matrix Multiplication Algorithm on a Distributed-Memory Parallel Computer, Using Overlapped Communication*, R. Agarwal, F. Gustavson and M. Zubair, IBM Journal or Research and Development, Vol. 38, No. 6, pp. 673-681, 1994.*PUMMA: Parallel Universal Matrix Multiplication Algorithms on Distributed-Memory Concurrent Computers*, J. Choi, J. Dongarra and D. Walker, Concurrency: Practice and Experience, Vol. 6, No. 7, pp. 543-570, 1994.*Matrix Multiplication on the Intel Touchstone DELTA*, S. Huss-Lederman, E. Jacobson, A. Tsao and G. Zhang, Concurrency: Practice and Experience, Vol. 6, No. 7, pp. 571-594, 1994.*A Three-Dimensional Approach to Parallel Matrix Multiplication*, R. Agarwal, S. Balle, F. Gustavson, M. Joshi and P. Palkar, IBM Journal or Research and Development, Vol. 39, No. 5, pp. 575-582, 1995.*A High Performance Parallel Strassen Implementation*, B. Grayson and R. van de Geijn, Parallel Processing Letters, Vol. 6, No. 1, pp. 3-12, 1996.*Parallel Implementation of BLAS: General Techniques for Level 3 BLAS*, A. Chtchelkanova, J. Gunnels, G. Morrow, J. Overfelt and R. van de Geijn, Concurrency: Practice and Experience, Vol. 9, No. 9, pp. 837-857, 1997.*A Poly-Algorithm for Parallel Dense Matrix Multiplication on Two-Dimensional Process Grid Topologies*, J. Li, R. Falgout and A. Skjellum, Concurrency: Practice and Experience, Vol. 9, No. 5, pp. 345-389, 1997.*SUMMA: Scalable Universal Matrix Multiplication Algorithm*, R. van de Geijn and J. Watts, Concurrency: Practice and Experience, Vol. 9, No. 4, pp. 255-274, 1997.

### Parallel Triangular Solve

*Parallel Solution Triangular Systems on Distributed-Memory Multiprocessors*, M. Heath and C. Romine, SIAM Journal on Scientific and Statistical Computing, Vol. 9, pp. 558-588, 1988.*A Parallel Triangular Solver for a Distributed-Memory Multiprocessor*, G. Li and T. Coleman, SIAM Journal on Scientific and Statistical Computing, Vol. 9, No. 3, pp. 485-502, 1988.*A New Method for Solving Triangular Systems on Distributed-Memory Message-Passing Multiprocessor*, G. Li and T. Coleman, SIAM Journal on Scientific and Statistical Computing, Vol. 10, No. 2, pp. 382-396, 1989.*Parallel Triangular System Solving on a Mesh Network of Transputers*, R. Bisseling and J. van der Vorst, SIAM Journal on Scientific and Statistical Computing, Vol. 12, pp. 787-799, 1991.