Efficient implementation of interval matrix multiplication

• Main Author: Nguyen, Hong Diep
• Other Authors: 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
• Language: English
• Published: HAL CCSD 2010
• Subjects: interval arithmetic; interval matrix multiplication; efficiency; [INFO.INFO-AO]Computer Science [cs]/Computer Arithmetic; Iceland
• Online Access: https://hal.inria.fr/inria-00469472; https://hal.inria.fr/inria-00469472/document; https://hal.inria.fr/inria-00469472/file/NGUYEN_mat_prod.pdf

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.