This paper analyses the performance of several versions of a block parallel algorithm in order to apply Neville elimination in a distributed memory parallel computer. Neville elimination is a procedure to transform a square matrix A into an upper triangular one. This analysis must take into account the algorithm behaviour as far as execution time, efficiency and scalability are concerned. Special attention has been paid to the study of the scalability of the algorithms trying to establish the relationship existing between the size of the block and the performance obtained in this metric. It is important to emphasize the high efficiency achieved in the studied cases and that the experimental results confirm the theoretical approximation. Therefore, we have obtained a high predicting ability tool of analysis. Finally, we will present the elimination of Neville as an efficient tool in detecting point sources in cosmic microwave background maps.
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This is one of several papers published in Journal of Mathematical Chemistry, Special Issue: CMMSE 2010, with invited editorial contribution by Prof. Jesus Vigo-Aguiar.
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Alonso, P., Cortina, R., Ranilla, J. et al. An efficient and scalable block parallel algorithm of Neville elimination as a tool for the CMB maps problem. J Math Chem 50, 345–358 (2012). https://doi.org/10.1007/s10910-010-9769-0