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Hierarchical Matrices: A Context in Which New Features Are Vital
Abstract
In this chapter, the authors present hierarchical matrices, which are a powerful numerical tool that allows reducing to a logarithmic order both the storage needs and computational time in exchange for a controlled accuracy loss, thanks to the compression of part of the original data to form low-rank blocks. This type of matrices presents certain particularities due to the storage layout, the different blocks configurations, and a hierarchically and nested partitioned structure of blocks; the presence of dense and low-rank blocks of various dimensions; and the recursive nature of the algorithms that compute the h-algebra operations. Thanks to the programming model OmpSs-2 and specifically to two novel features it incorporates, a fair parallel efficiency based on task-parallelism can be achieved in shared memory environments.
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