Saddle-Point Problems and Their Iterative Solution
Published on 2. February 2019
Book
Paperback/Softback
XIV, 136 pages
978-3-030-01430-8 (ISBN)
Description
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 of algebraic methods for solving them, with an emphasis on iterative methods and preconditioning. The theoretical results presented here are complemented by a case study on potential fluid flow problem in a real world-application. This book is mainly intended for students of applied mathematics and scientific computing, but also of interest for researchers and engineers working on various applications. It is assumed that the reader has completed a basic course on linear algebra and numerical mathematics.
More details
Product info
Book
Series
Edition
2018
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
25 s/w Abbildungen, 12 farbige Abbildungen
Bibliographie
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 9 mm
Weight
242 gr
ISBN-13
978-3-030-01430-8 (9783030014308)
DOI
10.1007/978-3-030-01431-5
Schweitzer Classification
Other editions
Additional editions
Miroslav Rozlozník
Saddle-Point Problems and Their Iterative Solution
E-Book
11/2018
Birkhäuser
€48.14
Available for download
Person
Miroslav Rozlozník, Czech Academy of Science, Praha, Czech Republic
Content
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.