A paradigm for parallel matrix algorithms: Scalable cholesky

Lecture Notes in Computer Science

Volumn 3648, Issue , 2005, Pages 687-698

  Wise, David S ^a   Citro, Craig ^a   Hursey, Joshua ^a   Liu, Fang ^a   Rainey, Michael ^a  

^a INDIANA UNIVERSITY   (United States)

Author keywords

Cholesky factorization; Finalizer; Morton order; Quadtrees

Indexed keywords

COMPUTER PROGRAMMING; FUNCTIONS; MATRIX ALGEBRA; PERFORMANCE; PHILOSOPHICAL ASPECTS; PROBLEM SOLVING;

CHOLESKY FACTORIZATION; CONTROL STRUCTURES; MEMORY HIERARCHY; PROGRAMMING ALGORITHMS;

PARALLEL ALGORITHMS;

EID: 27144518219     PISSN: 03029743     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1007/11549468_76     Document Type: Conference Paper

References (23)

1. Chatterjee, S., Lebeck, A.R., Patnala, P.K., Thottenthodi, M.: Recursive array layouts and fast parallel matrix multiplication. IEEE Trans. Parallel Distrib. Syst. 13 (2002) 1105-1123 http://dx.doi.org/10.1109/TPDS.2002.1058095
2. Thiyagalingam, J., Beckmann, O., Kelly, P.H.J.: Is Morton layout competitive for large two-dimensional arrays, yet? Concur. Comput. Prac. Exper. (2004)
3. To appear in special issue on Compilers for Parallel Computing. http://www.doc.ic.ac.uk/~phjk/Publications/IsMortonYetCCPandE2004.pdf
4. Goto, K., van de Geijn, R.: On reducing TLB misses in matrix multiplication. FLAME Working Note 9, Univ. of Texas, Austin (2002) http://www.cs.utexaB.edu/users/flame/pubs/GOTO.ps.gs
5. Morton, G.M.: A computer oriented geodetic data base and a new technique in file sequencing. Technical report, IBM Ltd., Ottawa, Ontario (1966)
6. Drakenberg, P., Lundevall, F., Lisper, B.: An efficient semi-hierarchical array layout. In Lee, G., Yew, P.C., eds.: Interaction between Compilers and Computer Architectures. Volume 613 of Kluwer Intl. Series in Engineering and Computer Science. Kluwer, Deventer, Netherlands (2001) http://www.mrtc.mdh.se/publications/0313.pdf
7. Wise, D.S.: Ahnentafel indexing into Morton-ordered arrays, or matrix locality for free. In Bode, A., Ludwig, T., Karl, W., Wismüller, R., eds.: Euro-Par 2000 - Parallel Processing. Volume 1900 of Lecture Notes in Comput. Sci. Springer, Heidelberg (2000) 774-883 http://www.springerlink.com/link.asp?id=0pc0e9gfk4x9j5fa
8. Wise, D.S., Frens, J.D., Gu, Y., Alexander, G.A.: Language support for Morton-order matrices. Proc. 8th ACM SIGPLAN Symp. on Principles and Practice of Parallel Program., SIGPLAN Not. 36 (2001) 24-33 http://doi.acm.org/10.1145/379539.379559
9. Schrack, G.: Finding neighbors of equal size in linear quadtrees and octrees in constant time. CVGIP: Image Underst. 55 (1992) 221-230
10. Raman, R., Wise, D.S.: Converting to and from dilated integers. Submitted for publication (2004) http://www.cs.indiana.edu/~dawise/Arcee/castingDilated-comb.pdf
11. Frigo, M., Leiserson, C.E., Prokop, H., Ramachandran, S.: Cache-oblivious algorithms. In: Proc. 40th Ann. Symp. Foundations of Computer Science. IEEE Computer Soc. Press, Washington, DC (1999) 285-298 http://dx.doi.org/10.1109/SFFCS.1999.814600
12. Frens, J.D.: Matrix Factorization Using a Block-Recursive Structure and Block-Recursive Algorithms. PhD thesis, Indiana Univ., Bloomington (2002) http://www.cs.indiana.edu/cgi-bin/techreporta/TRNNN.cgi?trnum=TR568
13. Spieß, J.: Untersuchungen des Zeitgewinns durch neue Algorithmen zur Matrix-Multiplication. Computing 17 (1976) 23-36
14. Tocher, K.D.: The application of automatic computers to sampling experiments. J. Roy. Statist. Soc. Ser. B 16 (1954) 39-61 See pp. 53-55.
15. Johnson, D.S.: A theoretician's guide to the experimental analysis of algorithms. In Goldwasser, M.H., Johnson, D.S., McGeoch, C.C., eds.: Data Structures, Near Neighbor Searches, and Methodology: 5th & 6th DIMACS Implementation Challenges. Volume 59 of DIMACS Ser. Discrete Math. Theoret. Comput. Sci. Amer. Math. Soc., Providence (2002) 215-250 http://www.research.att.com/-dsj/papers.html
16. Whaley, R.C., Dongarra, J.J.: Automatically tuned linear algebra software. In: Proc. Supercomputing '98. IEEE Computer Soc. Press, Washington, DC (1998) 38 http://dx.doi.org/10.1109/SC.1998.10004
17. Intel Corp. Santa Clara, CA: Intel Math Kernel Library. (2003) http://www.intel.com/software/products/mkl/
18. LAM/MPI Bloomington, IN: www.lam-mpi.org. (2004)
19. InfiniBand Trade Assn. Portland, OR: www.infinibandta.org. (2004)
20. InfiniCon Systems King of Prussia, PA: www.infinicon.com. (2004)
21. Myricom Inc. Arcadia, CA: www.myri.com. (2004)
22. Quadrics Ltd. Bristol, UK: www.quadrics.com. (2004)
23. Quadrics Ltd. Bristol, UK: Quadrics Release of MPICH 1.24. (2004) www.quadric.com