Exploiting Data Sparsity for Large-Scale Matrix Computations

Kadir Akbudak, Hatem Ltaief, Aleksandr Mikhalev*, Ali Charara, Aniello Esposito, David Keyes

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

18 Scopus citations


Exploiting data sparsity in dense matrices is an algorithmic bridge between architectures that are increasingly memory-austere on a per-core basis and extreme-scale applications. In this work, we leverage the Hierarchical matrix Computations on Manycore Architectures (HiCMA) library in order to tackle this challenging problem by achieving significant reductions in time to solution and memory footprint, while preserving a specified accuracy requirement of the application. We have extended HiCMA to provide a high-performance implementation on distributed-memory systems of one of the most widely used matrix factorization in large-scale scientific applications, i.e., the Cholesky factorization. It employs the tile low-rank data format to compress the dense data-sparse off-diagonal tiles of the matrix. It then decomposes the matrix computations into interdependent tasks and relies on the dynamic runtime system StarPU for asynchronous out-of-order scheduling, while allowing high user productivity. Performance comparisons and memory footprint on matrix dimensions up to eleven million show a performance gain and memory saving of more than an order of magnitude for both metrics on thousands of cores, against state-of-the-art open-source and vendor optimized numerical libraries. This represents an important milestone in enabling large-scale matrix computations toward solving big data problems in geospatial statistics for climate/weather forecasting applications.

Original languageEnglish (US)
Title of host publicationEuro-Par 2018
Subtitle of host publicationParallel Processing - 24th International Conference on Parallel and Distributed Computing, Proceedings
EditorsMassimo Torquati, Marco Aldinucci, Luca Padovani
PublisherSpringer Verlag
Number of pages14
ISBN (Print)9783319969824
StatePublished - 2018
Event24th International European Conference on Parallel and Distributed Computing, Euro-Par 2018 - Turin, Italy
Duration: Aug 27 2018Aug 31 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11014 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference24th International European Conference on Parallel and Distributed Computing, Euro-Par 2018

Bibliographical note

Publisher Copyright:
© 2018, Springer International Publishing AG, part of Springer Nature.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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