An Algorithm-by-Blocks for SuperMatrix Band Cholesky Factorization

1. Anderson, E., Bai, Z., Demmel, J., Dongarra, J.E., DuCroz, J., Greenbaum, A., Hammarling, S., McKenney, A.E., Ostrouchov, S., Sorensen, D.: LAPACK Users Guide. SIAM, Philadelphia (1992)

   MATH  Google Scholar 

2. Bellens, P., Perez, J.M., Badia, R.M., Labarta, J.: CellSs: A programming model for the Cell BE architecture. In: SC 2006: Proceedings of the 2006 ACM/IEEE conference on Supercomputing, p. 86. ACM Press, New York (2006)

   Google Scholar 

3. Bientinesi, P., Gunnels, J.A., Myers, M.E., Quintana-Ortí, E.S., van de Geijn, R.A.: The science of deriving dense linear algebra algo- rithms. ACM Transactions on Mathematical Software 31(1), 1–26 (2005)

   Article  MathSciNet  MATH  Google Scholar 

4. Bientinesi, P., Quintana-Ortí, E.S., van de Geijn, R.A.: Repre- senting linear algebra algorithms in code: The FLAME application programming interfaces. ACM Trans. Math. Soft. 31(1), 27–59 (2005)

   Article  Google Scholar 

5. Buttari, A., Langou, J., Kurzak, J., Dongarra, J.: A class of par- allel tiled linear algebra algorithms for multicore architectures. LAPACK Working Note 191 UT-CS-07-600, University of Tennessee (September 2007)

   Google Scholar 

6. Buttari, A., Langou, J., Kurzak, J., Dongarra, J.: Parallel tiled qr factorization for multicore architectures. LAPACK Working Note 190 UT-CS- 07-598, University of Tennessee (July 2007)

   Google Scholar 

7. Chan, E., Quintana-Ortí, E., Quintana-Ortí, G., van de Geijn, R.: SuperMatrix out-of-order scheduling of matrix operations for SMP and multi-core architectures. In: SPAA 2007: Proceedings of the Nineteenth ACM Sym- posium on Parallelism in Algorithms and Architectures, pp. 116–126 (2007)

   Google Scholar 

8. Chan, E., Van Zee, F.G., Bientinesi, P., Quintana-Ortí, G., Quintana-Ortí, E.S., van de Geijn, R.: SuperMatrix: A multithreaded runtime scheduling system for algorithms-by-blocks. In: PPoPP 2008: Proceedings of the 13th ACM SIGPLAN symposium on Principles and practices of parallel programming. ACM Press, New York (to appear, 2008)

   Google Scholar 

9. Chan, E., Van Zee, F., van de Geijn, R., Quintana-Ortí, E.S., Quintana-Ortí, G.: Satisfying your dependencies with SuperMatrix. In: IEEE Cluster 2007, pp. 92–99 (2007)

   Google Scholar 

10. Chatterjee, S., Lebeck, A.R., Patnala, P.K., Thottethodi, M.: Recursive array layouts and fast matrix multiplication. IEEE Trans. on Parallel and Distributed Systems 13(11), 1105–1123 (2002)

    Article  Google Scholar 

11. Dongarra, J.J., Duff, I.S., Sorensen, D.C., van der Vorst, H.A.: Solving Linear Systems on Vector and Shared Memory Computers. SIAM, Philadelphia (1991)

    MATH  Google Scholar 

12. Elmroth, E., Gustavson, F., Gustavson, F., Jonsson, I., Kagstrom, B.: Recursive blocked algorithms and hybrid data structures for dense matrix library software. SIAM Review 46(1), 3–45 (2004)

    Article  MathSciNet  MATH  Google Scholar 

13. Henry, G.: BLAS based on block data structures. Theory Center Technical Report CTC92TR89, Cornell University (February 1992)

    Google Scholar 

14. Leiserson, C., Plaat, A.: Programming parallel applications in Cilk. SIAM News, SINEWS (1998)

    Google Scholar 

15. Low, T.M., van de Geijn, R.: An API for manipulating matrices stored by blocks. Technical Report TR-2004-15, Department of Computer Sciences, The University of Texas at Austin (May 2004)

    Google Scholar 

16. Park, N., Hong, B., Prasanna, V.K.: Tiling, block data layout, and memory hier- archy performance. IEEE Trans. on Parallel and Distributed Systems 14(7), 640–654 (2003)

    Article  Google Scholar 

17. Quintana-Ortí, G., Quintana-Ortí, E., Chan, E., Van Zee, F.G., van de Geijn, R.: Scheduling of QR factorization algorithms on SMP and multi-core architectures. In: 16th Euromicro Int. Conference on Parallel, Dis- tributed and Network-based Processing. IEEE, Los Alamitos (to appear, 2008)

    Google Scholar 

18. Quintana-Ortí, G., Quintana-Ortí, E.S., Chan, E., van de Geijn, R., Van Zee, F.G.: Design and scheduling of an algorithm-by-blocks for the LU factorization on multithreaded architectures. FLAME Working Note #26 TR-07-50, The University of Texas at Austin, Department of Computer Sciences (September 2007)

    Google Scholar 

19. Quintana-Ortí, G., Quintana-Ortí, E.S., Remón, A., van de Geijn, R.: SuperMatrix for the factorization of band matrices. FLAMEWorking Note #27 TR-07-51, The University of Texas at Austin, Department of Computer Sciences (September 2007)

    Google Scholar 

20. Remón, A., Quintana-Ortí, E.S., Quintana-Ortí, G.: Cholesky factorization of band matrices using multithreaded BLAS. In: Kågström, B., Elmroth, E., Dongarra, J., Waśniewski, J. (eds.) PARA 2006. LNCS, vol. 4699, pp. 608–616. Springer, Heidelberg (to appear, 2007)

    Chapter  Google Scholar 

Download references