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Sistemi lineari

  • Alfio Quarteroni
  • Fausto Saleri
  • Paola Gervasio
Chapter
  • 1.3k Downloads
Part of the UNITEXT book series (UNITEXT, volume 105)

Astratto

In questo capitolo ci interessiamo ad un problema fondamentale del Calcolo Scientifico, quello della risoluzione numerica di sistemi algebrici lineari di grandi dimensioni. Dopo aver introdotto alcuni esempi motivati da applicazioni di grande rilievo, introduciamo i metodi diretti di fattorizzazione, seguiti dai metodi iterativi classici e da quelli moderni di tipo gradiente, gradiente coniugato e di Krylov per il caso non simmetrico. Grande attenzione è rivolta al caso di sistemi mal condizionati, alla loro risoluzione efficiente attraverso tecniche di precondizionamento ed all’analisi della loro stabilità rispetto a perturbazioni sui dati del problema (i coefficienti della matrice e/o le componenti del termine noto).

Un’analisi critica di confronto fra tecniche di fattorizzazione e tecniche iterative è sviluppata con particolare attenzione al caso di sistemi di grandi dimensioni e con matrice sparsa. Il capitolo si conclude con la proposta di numerosi esercizi.

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Copyright information

© Springer-Verlag Italia Srl. 2017

Authors and Affiliations

  • Alfio Quarteroni
    • 2
    • 1
  • Fausto Saleri
    • 3
  • Paola Gervasio
    • 4
  1. 1.École Polytechnique Fédérale (EPFL)LausanneSwitzerland
  2. 2.Politecnico di MilanoMilanItaly
  3. 3.MOXPolitecnico di MilanoMilanItaly
  4. 4.DICATAMUniversità degli Studi di BresciaBresciaItaly

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