Saddle-Point Problems and Their Iterative Solution

• Main Author: Rozložník, Miroslav (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2018.
• Edition: 1st ed. 2018.
• Series: Nečas Center Series,
• Subjects: Numerical analysis.; Numerical Analysis.

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...

Table of Contents:

• 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.