Abstract
This paper presents a parallel algorithm to solve linear equation systems. This method, known as Neville elimination, is appropriate especially for the case of totally positive matrices (all its minors are non-negative). We discuss one common way to partition coefficient matrix among processors. In our mapping, called columwise block-cyclic-striped mapping, the matrix is divided into blocks of complete columns and these blocks are distributed among the processors in a cyclic way. The theoretic asymptotic estimation assures the speed-up to be k (being k the processor number); so the efficiency can take the value 1. Furthermore, in order to study the performance of the algorithm over a real machine (IBM SP2), some constants have been estimated. If such constants take these experimental values, then theoretic results are confirmed.
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References
Alonso, P., Gasca, M., Peña, J.M.: Backward error analysis of Neville elimination, Applied Numerical Mathematics 23 (1997) 193–204
Alonso, P., Gasca, M., Peña, J.M.: Estudio del error progresivo en la eliminación de Neville, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid 92-1 (1998) 1–8
Alonso, P., Cortina, R., Ranilla, J.: Block-Striped Partitioning and Neville Elimination, EURO-PAR’99. Parallel Processing, Lecture Notes in Computer Science 1685 (1999) 1073–1077
Alonso, P., Cortina, R., Hernández, V., Ranilla, J.: A Study the performance of Neville elimination using two kinds of partitioning techniques. Linear Algebra and its Applications 332–334 (2001) 111–117
Gallivan, K. A., Plemmons, R. J., Sameh, A. H.: Paralell algorithms for dense linear algebra computations, SIAM Rev. 32 (1990) 54–135
Gasca, M., Michelli, C. A.: Total positivity and its Applications, Kluwer Academic Publishers, Boston (1996)
Gasca, M., Peña, J.M.: Total positivity and Neville elimination, Linear Algebra Appl. 165 (1992) 25–44
Hockney, R., Berry, M.: Public International Benchmarks for Parallel Computers. PARKBENCH Committee: Report (1996) (http://www.netlib.org//parkbench)
Kumar, V., Grama, A., Gupta, A., Karypis, G.: Introduction to Parallel Computing. Design and Analysis of Algorithms, The Benjamin/Cummings, Menlo Park, CA (1994)
Petitet, A.P., Dongarra, J.J.: Algorithmic Redistribution Methods for Block Cyclic Decompositions, submmited to IEEE Transactions on Parallel and Distributed Computing
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)
Trefethen, L. N., Schreiber, R. S.: Average-case stability of Gaussian Elimination SIAM J. Matrix Anal. Appl. 11 (1990) 335–360
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Alonso, P., Cortina, R., Díaz, I., Hernández, V., Ranilla, J. (2002). A Columnwise Block Striping in Neville Elimination. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_42
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DOI: https://doi.org/10.1007/3-540-48086-2_42
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