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However, the complex structure of such hierarchical matrices makes them difficult to parallelize. The block size and ranks can vary between the sub-blocks, which creates load imbalance. The dependency between the sub-blocks during factorization results in serialization. Since many sub-blocks are low-rank, their small computational load exposes the overhead of runtime systems. The combination of these factors makes it challenging to implement these methods on GPUs. In this work, we show that dense matrices can be factorized with linear complexity, while extracting the potential parallelism of GPUs. This is made possible through the [Formula: see text]-ULV factorization, which removes the dependency on trailing sub-matrices.<\/jats:p>","DOI":"10.1177\/10943420241242021","type":"journal-article","created":{"date-parts":[[2024,4,3]],"date-time":"2024-04-03T08:00:46Z","timestamp":1712131246000},"page":"314-336","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":4,"title":["An inherently parallel \u210b\n                    <sup>2<\/sup>\n                    -ULV factorization for solving dense linear systems on GPUs"],"prefix":"10.1177","volume":"38","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4688-5644","authenticated-orcid":false,"given":"Qianxiang","family":"Ma","sequence":"first","affiliation":[{"name":"School of Computing, Tokyo Institute of Technology, Tokyo, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7573-7873","authenticated-orcid":false,"given":"Rio","family":"Yokota","sequence":"additional","affiliation":[{"name":"Global Scientific Information and Computing Center, Tokyo Institute of Technology, Tokyo, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2024,4,3]]},"reference":[{"key":"bibr1-10943420241242021","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-58667-02"},{"key":"bibr2-10943420241242021","unstructured":"Ambikasaran S (2013) Fast algorithms for dense numerical linear algebra and applications. 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