Saddle-Point Problems and Their Iterative Solution

This book provides essential lecture notes on solving large linear saddle-point systems, which arise in a wide range of applications and often pose computational challenges in science and engineering. The focus is on discussing the particular properties of such linear systems, and a large selection...

Πλήρης περιγραφή

Λεπτομέρειες βιβλιογραφικής εγγραφής
Κύριος συγγραφέας: Rozložník, Miroslav (Συγγραφέας, http://id.loc.gov/vocabulary/relators/aut)
Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
Γλώσσα:English
Έκδοση: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
Έκδοση:1st ed. 2018.
Σειρά:Nečas Center Series,
Θέματα:
Διαθέσιμο Online:Full Text via HEAL-Link
Πίνακας περιεχομένων:
  • Introductory remarks. Formulation of saddle-point problem
  • Applications leading to saddle-point problems. Augmented systems in least squares problems. Saddle point problems from the discretization of partial differential equations with constraints. Kuhn-Karush-Tucker (KKT) systems in interior-point methods
  • Properties of saddle point matrices. The inverse of a saddle-point matrix. Spectral properties of saddle-point matrices
  • Solution approaches for saddle-point problems. Schur complement reduction. Null-space projection method
  • Direct methods for symmetric indefinite systems. Direct solution of saddle-point problems
  • AIterative solution of saddle-point problems. Stationary iteration methods. Krylov subspace methods. Preconditioned Krylov subspace methods
  • Saddle-point preconditioners. Block diagonal and triangular preconditioners. Indefinite preconditioning
  • Implementation and numerical behavior of saddle-point solvers
  • Case study: Polluted undeground water flow modelling in porous media.