Geodesic
Sparse matrix storage formats and acceleration of iterative solution of linear algebraic systems with dense matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXV, Tome 405 (2012), pp. 24-39 
R. R. Akhunov; S. P. Kuksenko; V. K. Salov; T. R. Gazizov. Sparse matrix storage formats and acceleration of iterative solution of linear algebraic systems with dense matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXV, Tome 405 (2012), pp. 24-39. http://geodesic.mathdoc.fr/item/ZNSL_2012_405_a2/
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     author = {R. R. Akhunov and S. P. Kuksenko and V. K. Salov and T. R. Gazizov},
     title = {Sparse matrix storage formats and acceleration of iterative solution of linear algebraic systems with dense matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {24--39},
     year = {2012},
     volume = {405},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_405_a2/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In the paper, formulas for comparing sparse matrix storage formats are derived. An iterative algorithm for solving linear algebraic systems using the sparse row format for storing prefiltered preconditioners is designed. A modification of the sparse row format leading to 1.14–1.23 times speed-up for matrices of order 1000 is suggested. It is demonstrated that as opposed to the usual storage format, the sparse row format provides for 1.5–1.6 times speed-up in solving linear systems of orders 4800, 6000, and 8000. The use of the results obtained allows one to reduce both memory and time requirements in solving large-scale problems with dense matrices.

[1] T. R. Gazizov, S. P. Kuksenko, “Optimizatsiya dopuska obnuleniya pri reshenii SLAU iteratsionnymi metodami s predobuslovlivaniem v zadachakh vychislitelnoi elektrodinamiki”, Elektromagn. volny elektr. sistemy, 2004, no. 8, 26–28

[2] S. Pissanetski, Tekhnologiya razrezhennykh matrits, Mir, M., 1988 | MR

[3] J. R. Gilbert, C. B. Moler, R. Schreiber, “Sparse matrices in MATLAB: design and implementation”, SIAM J. Matrix Anal. Appl., 13:1 (1992), 333–356 | DOI | MR | Zbl

[4] M. Lujan, L. Freeman, J. Gurd, “Performance evaluation of storage formats for sparse matrices in fortran”, High Performance Computing and Communications (Munich, Germany, September 13–15, 2006), Springer, 2006, 160–169

[5] S. P. Kuksenko, T. R. Gazizov, Iteratsionnye metody resheniya sistemy lineinykh algebraicheskikh uravnenii s plotnoi matritsei, Tomskii gosudarstvennyi universitet, Tomsk, 2007

[6] M. Yu. Balandin, E. P. Shurina, Metody resheniya SLAU bolshoi razmernosti, Izd-vo NGTU, Novosibirsk, 2000

[7] Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM, 2003 | MR