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...
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| Médium: | Elektronický zdroj E-kniha |
| Jazyk: | angličtina |
| Vydáno: |
Cham :
Springer International Publishing,
2018.
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| Vydání: | 1st ed. 2018. |
| Edice: | Nečas Center Series,
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| Témata: | |
| ISBN: | 9783030014315 |
| ISSN: | 2523-3343 |
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Obsah:
- 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.