Abstract
In this paper we analyze the performance of the Neville method when a block-cyclic checkerboard partitioning is used. This partitioning can exploit more concurrency than the striped method because the matrix computation can be divided out among more processors than in the case of striping. Concretely, it divides the matrix into blocks and maps them in a cyclic way among the processors. The performance of this parallel system is measured in terms of efficiency, which in this case is close to one when the optimum block size is used and it is run on a Parallel PC Cluster.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ando, T.: Totally positive matrices. Linear Algebra Appl. 90, 165–219 (1987)
Alonso, P., Gasca, M., Peña, J.M.: Backward error analysis of Neville elimination. Appl. Numer. Math. 23, 193–204 (1997)
Alonso, P., Cortina, R., Ranilla, J.: Block-Striped partitioning and Neville elimination. In: Amestoy, P.R., Berger, P., Daydé, M., Duff, I.S., Frayssé, V., Giraud, L., Ruiz, D. (eds.) Euro-Par 1999. LNCS, vol. 1685, pp. 1073–1077. Springer, Heidelberg (1999)
Alonso, P., Cortina, R., Hernández, V., Ranilla, J.: Study the performance of Neville elimination using two kinds of partitioning techniques. Linear Algebra Appl. 334, 111–117 (2001)
Alonso, P., Cortina, R., Díaz, I., Hernández, V., Ranilla, J.: A Columnwise Block Striping in Neville Elimination. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds.) PPAM 2001. LNCS, vol. 2328, pp. 379–386. Springer, Heidelberg (2002)
Alonso, P., Cortina, R., Díaz, I., Hernández, V., Ranilla, J.: A Simple Cost-Optimal parallel algorithm to solve linear equation systems. International Journal of Information 6(3), 297–304 (2003)
Dongarra, J.J.: Performance of Various Computers Using Standard Linear Equations Software (Linpack Benchmark Report), University of Tennessee Computer Science Technical Report, CS-89-85 (2001)
Gasca, M., Mühlbach, G.: Elimination techniques: from extrapolation to totally positive matrices and CAGD. J. Comput. Appl. Math. 122, 37–50 (2000)
Gasca, M., Peña, J.M.: Total positivity and Neville elimination. Linear Algebra Appl. 165, 25–44 (1992)
Gasca, M., Peña, J.M.: A matricial description of Neville elimination with applications to total positivity. Linear Algebra Appl. 202, 33–45 (1994)
Golub, G.H., Van Loan, C.F.: Matrix computations. Johns Hopkins, Baltimore (1989)
Kumar, V., Grama, A., Gupta, A., Karypis, G.: Introduction to Parallel Computing. In: Design and Analysis of Algorithms, The Benjamin/Cummings (1994)
Petitet, A.P., Dongarra, J.J.: Algorithmic Redistribution Methods for Block Cyclic Decompositions. IEEE T. Parall. Distr. 10, 201–220 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Abascal, P., Alonso, P., Cortina, R., Díaz, I., Ranilla, J. (2004). Analyzing the Efficiency of Block-Cyclic Checkerboard Partitioning in Neville Elimination. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2003. Lecture Notes in Computer Science, vol 3019. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24669-5_124
Download citation
DOI: https://doi.org/10.1007/978-3-540-24669-5_124
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21946-0
Online ISBN: 978-3-540-24669-5
eBook Packages: Springer Book Archive