Efficient implementation of interval matrix multiplication
International audience The straightforward implementation of interval matrix product suf- fers from poor efficiency, far from the performances of highly optimized floating-point implementations. In this paper, we show how to reduce the interval matrix multiplication to 9 floating-point matrix produc...
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ftccsdartic:oai:HAL:inria-00469472v1 2023-05-15T16:47:54+02:00 Efficient implementation of interval matrix multiplication Nguyen, Hong Diep Computer arithmetic (ARENAIRE) Inria Grenoble - Rhône-Alpes Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP) École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS) Reykjavik, Iceland 2010-06-06 https://hal.inria.fr/inria-00469472 https://hal.inria.fr/inria-00469472/document https://hal.inria.fr/inria-00469472/file/NGUYEN_mat_prod.pdf en eng HAL CCSD inria-00469472 https://hal.inria.fr/inria-00469472 https://hal.inria.fr/inria-00469472/document https://hal.inria.fr/inria-00469472/file/NGUYEN_mat_prod.pdf info:eu-repo/semantics/OpenAccess Para 2010: State of the Art in Scientific and Parallel Computing https://hal.inria.fr/inria-00469472 Para 2010: State of the Art in Scientific and Parallel Computing, Jun 2010, Reykjavik, Iceland interval arithmetic interval matrix multiplication efficiency [INFO.INFO-AO]Computer Science [cs]/Computer Arithmetic info:eu-repo/semantics/conferenceObject Conference papers 2010 ftccsdartic 2021-09-12T01:00:21Z International audience The straightforward implementation of interval matrix product suf- fers from poor efficiency, far from the performances of highly optimized floating-point implementations. In this paper, we show how to reduce the interval matrix multiplication to 9 floating-point matrix products - for performance issues - without sacrificing the quality of the result. We show that, compared to the straightforward implementation, the overes- timation factor is at most 1.18. Conference Object Iceland Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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ftccsdartic |
language |
English |
topic |
interval arithmetic interval matrix multiplication efficiency [INFO.INFO-AO]Computer Science [cs]/Computer Arithmetic |
spellingShingle |
interval arithmetic interval matrix multiplication efficiency [INFO.INFO-AO]Computer Science [cs]/Computer Arithmetic Nguyen, Hong Diep Efficient implementation of interval matrix multiplication |
topic_facet |
interval arithmetic interval matrix multiplication efficiency [INFO.INFO-AO]Computer Science [cs]/Computer Arithmetic |
description |
International audience The straightforward implementation of interval matrix product suf- fers from poor efficiency, far from the performances of highly optimized floating-point implementations. In this paper, we show how to reduce the interval matrix multiplication to 9 floating-point matrix products - for performance issues - without sacrificing the quality of the result. We show that, compared to the straightforward implementation, the overes- timation factor is at most 1.18. |
author2 |
Computer arithmetic (ARENAIRE) Inria Grenoble - Rhône-Alpes Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP) École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL) Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS) |
format |
Conference Object |
author |
Nguyen, Hong Diep |
author_facet |
Nguyen, Hong Diep |
author_sort |
Nguyen, Hong Diep |
title |
Efficient implementation of interval matrix multiplication |
title_short |
Efficient implementation of interval matrix multiplication |
title_full |
Efficient implementation of interval matrix multiplication |
title_fullStr |
Efficient implementation of interval matrix multiplication |
title_full_unstemmed |
Efficient implementation of interval matrix multiplication |
title_sort |
efficient implementation of interval matrix multiplication |
publisher |
HAL CCSD |
publishDate |
2010 |
url |
https://hal.inria.fr/inria-00469472 https://hal.inria.fr/inria-00469472/document https://hal.inria.fr/inria-00469472/file/NGUYEN_mat_prod.pdf |
op_coverage |
Reykjavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
Para 2010: State of the Art in Scientific and Parallel Computing https://hal.inria.fr/inria-00469472 Para 2010: State of the Art in Scientific and Parallel Computing, Jun 2010, Reykjavik, Iceland |
op_relation |
inria-00469472 https://hal.inria.fr/inria-00469472 https://hal.inria.fr/inria-00469472/document https://hal.inria.fr/inria-00469472/file/NGUYEN_mat_prod.pdf |
op_rights |
info:eu-repo/semantics/OpenAccess |
_version_ |
1766037994299457536 |