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An Additive Multilevel Preconditioning Method

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(1)An Additive Multilevel Preconditioning Method Nathalie Marco, Bruno Koobus, Alain Dervieux. To cite this version: Nathalie Marco, Bruno Koobus, Alain Dervieux. An Additive Multilevel Preconditioning Method. [Research Report] RR-2310, INRIA. 1994. �inria-00074363�. HAL Id: inria-00074363 https://hal.inria.fr/inria-00074363 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. An Additive Multilevel Preconditioning Method Nathalie MARCO, Bruno KOOBUS and Alain DERVIEUX. N˚ 2310 Aoˆut 1994. PROGRAMME 6 Calcul scientifique, mode´lisation et logiciel nume´rique. ISSN 0249-6399. apport de recherche. 1994.

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(255) I 2M*M N  N ,D( = c V 2M*M N  N ( =   ¢R&¿S½PHegsGË{RVa{PHe`ZPwW&hmW^u»bcSegcW&ƒoƒb^ke`Zs2RVhÁƒoPSRUŸb^`ZY &,‰VJ‹ ,  lV &,‰VJˆ , = 9 $ E =  ˆ  $ &)( = , c4&) V A $ , &DM*M N ( = , Å À | h  Œ { ƒ $ ƒ  Z o h b s e  ŠVp—Zf¤UZh6W&hos Rbs{s¬_RUYKƒ$RUh{ZhViXc‡Rx¡¢iX„{Z¸ZPSPSRVP·WxPSZ9_W^`_ab^¹WiXZs´p—e`h iXWxZYKPSYKƒb^kc9eujqR&_@¡ WiS egRV$ hÁW&Y9hos WiX PHeV  pwWx) h{& s´p} ‚  „oZ hº ao,}cSegegchoTT&eu¤UË{ZRVh´a{³ PHe`ZPrYKRbs{Zc9WxcrsoZjmh{Zs6egHh &,ˆVJ[ ,Xp iX„{Z  Œ gc  $ „mW&c(iXRǟžZ—j oZs´p^gZfida{c±$ _RVV h{cSe`s{ZP$iX„{Z}YKRVh{RVTUPHe`sË{RVa{PHe`ZP±WxhqW^k»bcSe`c³—z_v„oZYKZc &,‰VJ‹ , W&h{< s &,‰oŠ ,<Ÿ$Z_RUYKTZ  = 9 $ E =  "%$ 

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(259) hU¤&cSWiv^`Wxa{ŸbZeuOc^keu,Qi*»Ue`c ³ ¡Ãa{h{_fiSe`RUhÉR&¡ pm‹   ³ R&iXZ   

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(268) . 1. Amplification factor. 0.9 0.8. Rho Rho = Rho = Rho = Rho = Rho = Rho = Rho = Rho = Rho = Rho. 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0. 0.5. 1. 1.5. 2. 2.5. = 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 = 1 3. 3.5. ´Ë egTVa{PSZ‡‰ ' !$ [ 

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(278) "() 1. Amplification factor. 0.9 0.8. Rho Rho 2 Rho 2 Rho 2 Rho 2 Rho 2 Rho 2 Rho 2 Rho 2 Rho 2 Rho. 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0. 0. Ëde`TUa{PSZ¶‘Q. 0.5. 1. 1.5. 2. 2 = = = = = = = = = 2. = 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 = 2. 2.5. 3. 3.5.

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