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.