Saddle-Point Problems and Their Iterative Solution

By Miroslav Rozložník

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.

• Format: Paperback
• Language: English
• ISBN: 3030014304
• ISBN13: 9783030014308
• Release Date: November 2018
• Publisher: Birkhauser
• Length: 136 Pages
• Weight: 0.49 lbs.
• Dimensions: 0.3" x 6.1" x 9.2"