A parallel matrix scaling algorithm

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5336 LNCS, Issue , 2008, Pages 301-313

  Amestoy, Patrick R ^a   Duff, Iain S ^b,c   Ruiz, Daniel ^a   Uçar, Bora ^c  

^a UNIVERSITÉ DE TOULOUSE   (France)

^b RAL   (United Kingdom)

^c CERFACS   (France)

Author keywords

Equilibration; Matrix scaling; Parallel computing; Sparse matrices

Indexed keywords

HIGH PERFORMANCE LIQUID CHROMATOGRAPHY; PARALLEL PROCESSING SYSTEMS;

COMPUTING ENVIRONMENTS; EQUILIBRATION; ITERATIVE PROCEDURES; MATRIX SCALING; PARALLEL COMPUTING; PARALLEL PERFORMANCES; PARALLELIZATION; SCALING ALGORITHMS; SPARSE MATRICES;

PARALLEL ALGORITHMS;

EID: 58349101743     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-92859-1_27     Document Type: Conference Paper

References (22)

1. Bisseling, R.H., Meesen, W.: Communication balancing in parallel sparse matrixvector multiplication. Electronic Transactions on Numerical Analysis 21, 47-65 (2005)
2. Bunch, J.R.: Equilibration of symmetric matrices in the max-norm. Journal of the ACM 18(4), 566-572 (1971)
3. Burns, G., Daoud, R., Vaigl, J.: LAM: an open cluster environment for MPI. In: Ross, J.W. (ed.) Proceedings of Supercomputing Symposium 1994, pp. 379-386. University of Toronto (1994)
4. Çatalyürek, Ü.V., Aykanat, C.: Hypergraph-partitioning based decomposition for parallel sparse-matrix vector multiplication. IEEE Transactions on Parallel and Distributed Systems 10(7), 673-693 (1999)
5. Çatalyürek, Ü.V., Aykanat, C.: PaToH: A multilevel hypergraph partitioning tool, version 3.0. Technical Report BU-CE-9915. Computer Engineering Department, Bilkent University (1999)
6. Çatalyiirek, Ü.V., Aykanat, C.: A fine-grain hypergraph model for 2d decomposition of sparse matrices. In: Proceedings of 15th International Parallel and Distributed Processing Symposium (IPDPS), San Francisco, CA (April 2001)
7. Curtis, A.R., Reid, J.K.: On the automatic scaling of matrices for Gaussian elimination. IMA Journal of Applied Mathematics 10(1), 118-124 (1972)
8. Davis, T.A.: University of Florida sparse matrix collection. NA Digest, 92/96/97, 1994/1996/1997, http://www.cise.uf1.edu/research/sparse/matrices
9. Dolan, E.D., Moré, J.J.: Benchmarking optimization software with performance profiles. Mathematical Programming 91(2). 201-213 (2002)
10. Duff, J.S., Erisman, A.M., Reid, J.K.: Direct Methods for Sparse Matrices. Oxford University Press, London (1986)
11. Duff, I.S., Koster, J.: On algorithms for permuting large entries to the diagonal of a sparse matrix. SIAM Journal on Matrix Analysis and Applications 22(4), 973-996 (2001)
12. Hendrickson, B., Kolda, T.G.: Partitioning rectangular and structurally unsymmetric sparse matrices for parallel processing. SIAM Journal on Scientific Computing 21(6), 2048-2072 (2000)
13. HSL: A collection of Fortran codes for large-scale scientific computation (2004), http://www.cse.scitech.ac.uk/nag/hsl
14. MPI: A Message-Passing Interface Standard, Version 2.1 (2008), http://www.mpi-forum.org/docs/
15. Rothblum, U.G., Schneider, H., Schneider, M.H.: Scaling matrices to prescribed row and column maxima. SIAM Journal on Matrix Analysis and Applications 15(1), 1-14 (1994)
16. Ruiz, D.: A scaling algorithm to equilibrate both rows and columns norms in matrices. Technical Report RAL-TR-2001-034 and RT/APO/01/4, Rutherford Appleton Laboratory, Oxon, UK and ENSEEIHT-IRIT, Toulouse, France (2001)
17. Schneider, M.H., Zenios, S.: A comparative study of algorithms for matrix balancing. Operations Research 38(3), 439-455 (1990)
18. Sinkhorn, R., Knopp, P.: Concerning nonnegative matrices and doubly stochastic matrices. Pacific Journal of Mathematics 21(2), 343-348 (1967)
19. Sterling, T., Savarese, D., Becker, D.J., Dorband, J.E., Ranaweke, U.A., Packer, C.V.: BEOWULF: A parallel workstation for scientific computation. In: Proceedings of the 24th International Conference on Parallel Processing (1995)
20. Uçar, B., Aykanat, C.: Encapsulating multiple communication-cost metrics in partitioning sparse rectangular matrices for parallel matrix-vector multiplies. SIAM Journal on Scientific Computing 25(6), 1827-1859 (2004)
21. Uçar, B., Aykanat, C.: Revisiting hypergraph models for sparse matrix partitioning. SIAM Review 49(4), 595-603 (2007)
22. Vastenhouw, B., Bisseling, R.H.: A two-dimensional data distribution method for parallel sparse matrix-vector multiplication. SIAM Review 47(1), 67-95 (2005)