English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this work, we consider the reformulation of hierarchical ($\mathcal{H}$)matrix algorithms for many-core processors with a model implementation ongraphics processing units (GPUs). $\mathcal{H}$ matrices approximate specificdense matrices, e.g., from discretized integral equations or kernel ridgeregression, leading to log-linear time complexity in dense matrix-vectorproducts. The parallelization of $\mathcal{H}$ matrix operations on many-coreprocessors is difficult due to the complex nature of the underlying algorithms.While previous algorithmic advances for many-core hardware focused onaccelerating existing $\mathcal{H}$ matrix CPU implementations by many-coreprocessors, we here aim at totally relying on that processor type. As maincontribution, we introduce the necessary parallel algorithmic patterns allowingto map the full $\mathcal{H}$ matrix construction and the fast matrix-vectorproduct to many-core hardware. Here, crucial ingredients are space fillingcurves, parallel tree traversal and batching of linear algebra operations. Theresulting model GPU implementation hmglib is the, to the best of the authorsknowledge, first entirely GPU-based Open Source $\mathcal{H}$ matrix library ofthis kind. We conclude this work by an in-depth performance analysis and acomparative performance study against a standard $\mathcal{H}$ matrix library,highlighting profound speedups of our many-core parallel approach.

Algorithmic patterns for $\mathcal{H}$-matrices on many-core processors