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Many dense linear algebra problems can be replaced by hierarchical low-rank approximation of the dense matrices, which results in much better asymptotic complexity for both arithmetic and storage requirements. These methods also possess favorable characteristics for extreme scale computing, such as high asynchronicity, controllable arithmetic intensity, and an inherently hierarchical data structure. However, these algorithms are complicated and difficult to implement compared to standard linear algebra algorithms. This presentation will cover a few of the important issues for getting hierarchical low-rank approximation codes to scale on future architectures.
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