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Matrices Structurées Et Matrices de Toeplitz Par Blocs de Toeplitz by Khalil-H

Matrices Structurées Et Matrices de Toeplitz Par Blocs de Toeplitz

by Khalil-H
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Book cover type: Paperback
  • ISBN13: 9786131530937
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 136
  • Original Price: GBP 40.0
  • Language: French
  • Edition: N/A
  • Item Weight: 209 grams
  • BISAC Subject(s): General

Plusieurs problèmes en mathématiques appliquées requièrent la résolution de systèmes linéaires de très grandes tailles, et parfois ces systèmes doivent ètre résolus de multiples fois. Dans des tels cas, les algorithmes standards basés sur l'élimination de Gauss demandent O(n 3) opérations arithmétiques pour résoudre un système de taille n, qui sera un handicap pour le calcul. C'est pour cela qu'on cherche à utiliser la structure pour réduire le temps de calcul. La structure de Toeplitz, de Hankel, de Cauchy, de Vandermonde et d'autre structure plus générales sont bien exploitées pour réduire la complexité de résolution d'un système linéaire à O(n log 2 n) opérations arithmétiques. Les matrices structurées en deux niveaux et surtout les matrices de Toeplitz par blocs de Toeplitz (TBT) apparaissent dans beaucoup des applications. La difficulté de généraliser la notion de rang de déplacement au cas biniveaux est à l'origine de l'absence des algorithmes rapides de résolutions des systèmes TBT. Dans ce travail on décrit ces dificultés, et on décrit des nouveaux algorithmes rapides de résolution des systèmes TBT de grandes tailles.

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