For a given linear algebra problem, we consider those solution algorithms that are mathematically equivalent to one another, and that mostly consist of a sequence of callsto kernels from optimized libraries such as BLAS and LAPACK. Although equivalent (at least in exact precision) , those algorithms typically exhibit significant differences in terms of performance , and naturally, we are interested in finding the fastest one(s) . In practice, we often observe that multiple algorithms yield comparable performance characteristics. Therefore , we aim to identify  the subset of algorithms  that are reliably faster than the rest.  To this end, instead of  quantifying the performance of an algorithm in absolute terms, we present a measurement-based approach that assigns a relative score to the algorithms in comparison to one another. The relative performance is encoded by sorting the algorithms based on pair-wise comparisons and  ranking them into equivalence classes, where more than one algorithm can obtain the same rank. We show that the relative performance leads to robust identification of the fastest algorithms, that is, reliable identifications even with noisy system conditions 
In scientific computing, it is common that one target computation can be translated into many different sequences of library calls, each identifying an algorithm. Although mathematically equivalent , those algorithms might exhibit significant differences in terms of performance . In practice, we observe that subsets of algorithms show comparable performance characteristics. For this reason , we aim to identify and separate not one algorithm, but the subset of algorithms , that are reliably faster than the rest. One of the motivations for this setup is that it makes it then possible to select an algorithm based on additional performance metrics such as those based on energy or scalability. To this end, instead of using the usual methods of quantifying the performance of an algorithm in absolute terms, we present a measurement-based approach that assigns a relative score to the algorithms in comparison to one another. The relative performance is encoded by sorting the algorithms based on pair-wise comparisons and by ranking them into equivalence (or performance) classes, so that multiple algorithms can obtain the same rank. We show that this approach, based on relative performance, leads to robust identification of the fastest algorithms, that is, reliable identification even under noisy system conditions .
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For a given linear algebra problem, we consider those solution algorithms that are mathematically equivalent to one another, and that mostly consist of a sequence of callsto kernels from optimized libraries such as BLAS and LAPACK. Although equivalent (at least in exact precision)
In scientific computing, it is common that one target computation can be translated into many different sequences of library calls, each identifying an algorithm. Although mathematically equivalent
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typically
might
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, and naturally, we are interested in finding the fastest one(s)
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often observe that multiple algorithms yield
observe that subsets of algorithms show
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Therefore
For this reason
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and separate not one algorithm, but
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,
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One of the motivations for this setup is that it makes it then possible to select an algorithm based on additional performance metrics such as those based on energy or scalability.
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using the usual methods of
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by
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classes, where more than one algorithm
(or performance) classes, so that multiple algorithms
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the relative performance
this approach, based on relative performance,
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identifications even with
identification even under
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.