Abstract. In simulations of supernovae, linear systems of equations with a block penta-diagonal matrix possessing small, dense matrix blocks occur. For an efficient solution, a compact multiplication scheme based on a restructured version of the Thomas algorithm and specifically adapted routines for LU factorization as well as forward and backward substitution are presented. On a NEC SX-8 vector system, runtime could be decreased between 35% and 54% for block sizes varying from 20 to 85 compared to the original code with BLAS and LAPACK routines.

Abstract-When an adaptive software component is employed to select the best-performing implementation for a communication operation at runtime, the correctness of the decision taken strongly depends on detecting and removing outliers in the data used for the comparison. This automatic decision is greatly complicated by the fact that the types and quantities of outliers depend on the network interconnect and the nodes assigned to the job by the batch scheduler. This paper evaluates four different statistical methods used for handling outliers, namely a standard interquartile range method, a heuristic derived from the trimmed mean value, cluster analysis and a method using robust statistics. Using performance data from the Abstract Data and Communication Library (ADCL) we evaluate the correctness of the decisions made with each statistical approach over three fundamentally different network interconnects, namely a highly reliable InfiniBand network, a Gigabit Ethernet network having a larger variance in the performance, and a hierarchical Gigabit Ethernet network.

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