The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
La conception de processeurs matriciels pour résoudre des systèmes linéaires en utilisant la méthode d'élimination gaussienne sans division en deux étapes est envisagée. La méthode en deux étapes peut être utilisée pour améliorer les systèmes basés sur la méthode en une étape en termes de stabilité numérique ainsi que les exigences de haute précision. Malgré les calculs assez compliqués nécessaires à chaque itération de la méthode en deux étapes, nous développons un algorithme parallèle innovant dont le graphe de dépendance des données répond aux exigences de régularité et de localité. Ensuite, nous dérivons des processeurs matriciels bidimensionnels en adoptant une approche systématique pour étudier l'ensemble de toutes les solutions admissibles et obtenir les processeurs matriciels optimaux sous une planification espace-temps linéaire. Les processeurs matriciels sont optimaux en termes de nombre d'éléments de traitement utilisés.
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Shietung PENG, Stanislav G. SEDUKHIN, "Design of Optimal Array Processors for Two-Step Division-Free Gaussian Elimination" in IEICE TRANSACTIONS on Information,
vol. E82-D, no. 12, pp. 1503-1511, December 1999, doi: .
Abstract: The design of array processors for solving linear systems using two-step division-free Gaussian elimination method is considered. The two-step method can be used to improve the systems based on the one-step method in terms of numerical stability as well as the requirements for high-precision. In spite of the rather complicated computations needed at each iteration of the two-step method, we develop an innovative parallel algorithm whose data dependency graph meets the requirements for regularity and locality. Then we derive two-dimensional array processors by adopting a systematic approach to investigate the set of all admissible solutions and obtain the optimal array processors under linear time-space scheduling. The array processors is optimal in terms of the number of processing elements used.
URL: https://global.ieice.org/en_transactions/information/10.1587/e82-d_12_1503/_p
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@ARTICLE{e82-d_12_1503,
author={Shietung PENG, Stanislav G. SEDUKHIN, },
journal={IEICE TRANSACTIONS on Information},
title={Design of Optimal Array Processors for Two-Step Division-Free Gaussian Elimination},
year={1999},
volume={E82-D},
number={12},
pages={1503-1511},
abstract={The design of array processors for solving linear systems using two-step division-free Gaussian elimination method is considered. The two-step method can be used to improve the systems based on the one-step method in terms of numerical stability as well as the requirements for high-precision. In spite of the rather complicated computations needed at each iteration of the two-step method, we develop an innovative parallel algorithm whose data dependency graph meets the requirements for regularity and locality. Then we derive two-dimensional array processors by adopting a systematic approach to investigate the set of all admissible solutions and obtain the optimal array processors under linear time-space scheduling. The array processors is optimal in terms of the number of processing elements used.},
keywords={},
doi={},
ISSN={},
month={December},}
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TY - JOUR
TI - Design of Optimal Array Processors for Two-Step Division-Free Gaussian Elimination
T2 - IEICE TRANSACTIONS on Information
SP - 1503
EP - 1511
AU - Shietung PENG
AU - Stanislav G. SEDUKHIN
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Information
SN -
VL - E82-D
IS - 12
JA - IEICE TRANSACTIONS on Information
Y1 - December 1999
AB - The design of array processors for solving linear systems using two-step division-free Gaussian elimination method is considered. The two-step method can be used to improve the systems based on the one-step method in terms of numerical stability as well as the requirements for high-precision. In spite of the rather complicated computations needed at each iteration of the two-step method, we develop an innovative parallel algorithm whose data dependency graph meets the requirements for regularity and locality. Then we derive two-dimensional array processors by adopting a systematic approach to investigate the set of all admissible solutions and obtain the optimal array processors under linear time-space scheduling. The array processors is optimal in terms of the number of processing elements used.
ER -