LU factorization on heterogeneous systems: an energy-efficient approach towards high performance

1. Luciani X, Albera L (2015) Joint eigenvalue decomposition of non-defective matrices based on the LU factorization with application to ICA. IEEE Trans Signal Process 63(17):1

   Article  MathSciNet  Google Scholar 

2. Petitet A, Whaley RC, Dongarra J, Cleary A (2004) HPL-a portable implementation of the high-performance linpack benchmark for distributed-memory computers. http://www.netlib.org/benchmark/hpl/

3. http://www.top500.org

4. Castaldo AM, Clint Whaley R, Samuel S (2010) Scaling LAPACK panel operations using parallel cache assignment. ACM Trans Math Softw 45(5):223–232

   MATH  Google Scholar 

5. Xu W, Lu Y, Li Q, Zhou E, Song Z, Dong Y, Zhang W (2014) Hybrid hierarchy storage system in MilkyWay-2 supercomputer. Front Comput Sci 8(3):367–377

6. Kogge P, Borkar S, Dan C, Carlson W, Dally W, Denneau M, Franzon P, Harrod W, Hiller J, Stephen K (2008) Exascale computing study: technology challenges in achieving exascale systems. DARPA Information Processing Techniques Office

7. Heinecke A, Vaidyanathan K, Smelyanskiy M, Kobotov A, Dubtsov R, Henry G, Shet AG, Chrysos G, Dubey P (2013) Design and implementation of the Linpack benchmark for single and multi-node systems based on Intel Xeon Phi coprocessor. In: 2013 IEEE 27th international symposium on parallel and distributed processing (IPDPS), pp 126–137

8. Fatica M (2009) Accelerating linpack with CUDA on heterogenous clusters. In: Proceedings of 2nd workshop on general purpose processing on graphics processing units, GPGPU-2, pp 46–51

9. Endo T, Matsuoka S, Nukada A, Maruyama N (2010) Linpack evaluation on a supercomputer with heterogeneous accelerators. In: 2010 IEEE international symposium on parallel and distributed processing (IPDPS), pp 1–8

10. Jo Gangwon, Nah Jeongho, Lee Jun, Kim Jungwon, Lee Jaejin (2015) Accelerating LINPACK with MPI-OpenCL on clusters of multi-GPU nodes. IEEE Trans Parallel Distrib Syst 26:1

    Article  Google Scholar 

11. Wang F, Yang CQ, Du YF, Chen J, Yi HZ, Xu WX (2011) Optimizing linpack benchmark on GPU-accelerated petascale supercomputer. J Comput Sci Technol 26(5):854–865

    Article  Google Scholar 

12. Kurzak J, Luszczek P, Faverge M, Dongarra J (2013) LU factorization with partial pivoting for a multicore system with accelerators. IEEE Trans Parallel Distrib Syst 24(24):1613–1621

    Article  Google Scholar 

13. Deisher M, Smelyanskiy M, Nickerson B, Lee VW, Chuvelev M, Dubey P (2011) Designing and dynamically load balancing hybrid LU for multi/many-core. Comput Sci Res Dev 26(3–4):211–220

    Article  Google Scholar 

14. Chen X, Chang LW, Rodrigues CI, Lv J, Wang Z, Hwu WM (2015) Adaptive cache management for energy-efficient GPU computing. In: Proceedings of the 47th annual IEEE/ACM international symposium on microarchitecture, pp 343–355

15. Dongarra JJ, Duff LS, Sorensen DC, Vander Vorst HA (1998) Numerical linear algebra for high-performance computers. Society for Industrial and Applied Mathematics, Siam

16. Gustavson FG (1997) Recursion leads to automatic variable blocking for dense liner algebra algorithms. IBM J Res Dev 41(6):737–755

    Article  Google Scholar 

17. Van De Velde EF (1990) Experiments with multicomputer LU-decomposition. Concurr Pract Exper 2(1):1–6

    Article  Google Scholar 

18. Fox GC, Johnson MA, Lyzenga GA, Otto SW, Salmon JK, Walker DW (1988) Solving problems on concurrent processors. Vol. 1: general techniques and regular problems, Prentice Hall, Old Tappan

19. Hipes PG, Kuppermann A (1989) Gauss–Jordan inversion with pivoting on the caltech mark ii hypercube. In: Hypercube concurrent computers and applications, pp 1621–1634

20. Bach M, Kretz M, Lindenstruth V, Rohr D (2011) Optimized HPL for AMD GPU and multi-core CPU usage. Comput Sci Res Dev 26(3):153–164

    Article  Google Scholar 

21. Michael K, Gunnels J, Brokenshire D, Benton B (2009) Petascale computing with accelerators. In: Proceedings of the 14th ACM SIGPLAN symposium on principles and practice of parallel programming, PPoPP’09, pp 241–250

22. Dongarra J, Gates M, Haidar A, Jia Y, Kabir K, Luszczek P, Tomov S (2013) Portable HPC programming on intel many-integrated-core hardware with MAGMA Port to Xeon Phi. In: International conference on parallel processing and applied mathematics, Springer, pp 571–581

23. Beckingsale D, Gaudin W, Herdman A, Jarvis S (2015) Resident block-structured adaptive mesh refinement on thousands of graphics processing units. In: 2015 44th international conference on parallel processing (ICPP), pp 61–70

24. Tan L, Kothapalli S, Chen L, Hussaini O, Bissiri R, Chen Z (2014) A survey of power and energy efficient techniques for high performance numerical linear algebra operations. In: Parallel Comput, December 2014

25. Haidar A, Dong T, Luszczek P, Tomov S, Dongarra J (2015) Optimization for performance and energy for batched matrix computations on GPUs. In: Proceedings of the 8th workshop on general purpose processing uGPUs, GPGPU-8, pp 59–69

26. Haidar A, Dong T, Tomov S, Luszczek P, Dongarra J (2015) Framework for batched and gpu-resident factorization algorithms to block householder transformations. In: ISC high performance, pp 07–25

27. Liu C, Li J, Huang W, Rubio J, Speight E, Lin X (2012) Power-efficient time-sensitive mapping in heterogeneous systems. In: Proceedings of the 21st international conference on parallel architectures and compilation techniques, PACT ’12, pp 23–32

28. Hong S, Kim H (2010) An integrated gpu power and performance model. In: Proceedings of the 37th annual international symposium on computer architecture, ISCA ’10, pp 280–289

29. Alonso P, Dolz MF, Igual FD, Mayo R, Quintana-Ort ES (2012) Reducing energy consumption of dense linear algebra operations on hybrid CPU–GPU platforms. In: 2012 IEEE 10th international symposium on parallel and distributed processing with applications, pp 56–62

30. Intel Math Kernel Library (Intel MKL)

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