@book {, title = {Parallel Processing and Applied Mathematics: 13th International Conference, PPAM 2019, Bialystok, Poland, September 8{\textendash}11, 2019, Revised Selected Papers, Part II}, series = {Lecture Notes in Computer Science}, number = {12044}, year = {2020}, month = {2020-03}, pages = {503}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, isbn = {978-3-030-43222-5}, doi = {https://doi.org/10.1007/978-3-030-43222-5}, author = {Roman Wyrzykowski and Ewa Deelman and Jack Dongarra and Konrad Karczewski} } @book {, title = {Parallel Processing and Applied Mathematics: 13th International Conference, PPAM 2019, Bialystok, Poland, September 8{\textendash}11, 2019, Revised Selected Papers, Part I}, series = { Lecture Notes in Computer Science}, number = {12043}, year = {2020}, month = {2020-03}, pages = {581}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, edition = {1}, isbn = {978-3-030-43229-4}, doi = {https://doi.org/10.1007/978-3-030-43229-4}, author = {Roman Wyrzykowski and Ewa Deelman and Jack Dongarra and Konrad Karczewski} } @inbook {883, title = {Dense Symmetric Indefinite Factorization on GPU Accelerated Architectures}, booktitle = {Lecture Notes in Computer Science}, series = {11th International Conference, PPAM 2015, Krakow, Poland, September 6-9, 2015. Revised Selected Papers, Part I}, volume = {9573}, year = {2016}, month = {2015-09}, pages = {86-95}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, chapter = {Parallel Processing and Applied Mathematics}, abstract = {We study the performance of dense symmetric indefinite factorizations (Bunch-Kaufman and Aasen{\textquoteright}s algorithms) on multicore CPUs with a Graphics Processing Unit (GPU). Though such algorithms are needed in many scientific and engineering simulations, obtaining high performance of the factorization on the GPU is difficult because the pivoting that is required to ensure the numerical stability of the factorization leads to frequent synchronizations and irregular data accesses. As a result, until recently, there has not been any implementation of these algorithms on hybrid CPU/GPU architectures. To improve their performance on the hybrid architecture, we explore different techniques to reduce the expensive communication and synchronization between the CPU and GPU, or on the GPU. We also study the performance of an LDL^T factorization with no pivoting combined with the preprocessing technique based on Random Butterfly Transformations. Though such transformations only have probabilistic results on the numerical stability, they avoid the pivoting and obtain a great performance on the GPU. }, keywords = {Communication-avoiding, Dense symmetric indefinite factorization, gpu computation, randomization}, isbn = {978-3-319-32149-3}, doi = {10.1007/978-3-319-32149-3_9}, author = {Marc Baboulin and Jack Dongarra and Adrien Remy and Stanimire Tomov and Ichitaro Yamazaki}, editor = {Roman Wyrzykowski and Ewa Deelman and Konrad Karczewski and Jacek Kitowski and Kazimierz Wiatr} } @article {icl:727, title = {Parallel Processing and Applied Mathematics, 9th International Conference, PPAM 2011}, journal = {Lecture Notes in Computer Science}, volume = {7203}, year = {2012}, month = {2012-00}, address = {Torun, Poland}, editor = {Roman Wyrzykowski and Jack Dongarra and Konrad Karczewski and Jerzy Wasniewski} } @article {icl:722, title = {Reducing the Amount of Pivoting in Symmetric Indefinite Systems}, journal = {Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science (PPAM 2011)}, volume = {7203}, year = {2012}, month = {2012-00}, pages = {133-142}, publisher = {Springer-Verlag Berlin Heidelberg}, author = {Dulceneia Becker and Marc Baboulin and Jack Dongarra}, editor = {Roman Wyrzykowski and Jack Dongarra and Konrad Karczewski and Jerzy Wasniewski} } @inproceedings {icl:580, title = {8th International Conference on Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science (LNCS)}, journal = {PPAM 2009 Proceedings}, volume = {6067}, year = {2010}, month = {2010-09}, publisher = {Springer}, address = {Wroclaw, Poland}, editor = {Roman Wyrzykowski and Jack Dongarra and Konrad Karczewski and Jerzy Wasniewski} } @inproceedings {icl:452, journal = {7th International parallel Processing and Applied Mathematics Conference, Lecture Notes in Comptuer Science}, volume = {4967}, year = {2008}, month = {2008-01}, publisher = {Springer Berlin}, address = {Gdansk, Poland}, editor = {Roman Wyrzykowski and Jack Dongarra and Konrad Karczewski and Jerzy Wasniewski} }