Semi-Automatic Task Graph Construction for ℋ-Matrix Arithmetic
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A new method to construct task graphs for -matrix arithmetic is introduced, which uses the information associated with all tasks of the standard recursive -matrix algorithms, e.g., the block index set of the matrix blocks involved in the computation. Task refinement, i.e., the replacement of tasks by sub-computations, is then used to proceed in the -matrix hierarchy until the matrix blocks containing the actual matrix data are reached. This process is a natural extension of the classical, recursive way in which -matrix arithmetic is defined and thereby simplifies the efficient usage of many-core systems. Examples for standard and accumulator based -arithmetic are shown for model problems with different block structures.
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