A Columnwise Block Striping in Neville Elimination
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.
KeywordsGaussian Elimination Communication Time Total Positivity Positive Matrice Linear Equation System
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- 2.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) 1–8Google Scholar
- 8.Hockney, R., Berry, M.: Public International Benchmarks for Parallel Computers. PARKBENCH Committee: Report (1996) (http://www.netlib.org//parkbench)
- 9.Kumar, V., Grama, A., Gupta, A., Karypis, G.: Introduction to Parallel Computing. Design and Analysis of Algorithms, The Benjamin/Cummings, Menlo Park, CA (1994)Google Scholar
- 10.Petitet, A.P., Dongarra, J.J.: Algorithmic Redistribution Methods for Block Cyclic Decompositions, submmited to IEEE Transactions on Parallel and Distributed ComputingGoogle Scholar
- 11.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)Google Scholar