Saddle-Point Problems and Their Iterative ...

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Beschreibung

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.

Über den Autor

Miroslav Rozloník, Czech Academy of Science, Praha, Czech Republic

Zusammenfassung

Reviews classical results on the solution of saddle problems that appeared in books, articles and proceedings papers

Covers recent results on this subject achieved by the author and his colleagues

Presents a case study of the application of theoretical results in underground water flow modeling

Inhaltsverzeichnis

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.

Details

Erscheinungsjahr:	2018
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xiv 136 S. 25 s/w Illustr. 12 farbige Illustr. 136 p. 37 illus. 12 illus. in color.
ISBN-13:	9783030014308
ISBN-10:	3030014304
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Rozlo¿ník, Miroslav
Auflage:	1st edition 2018
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, D-14197 Berlin, juergen.hartmann@springer.com
Maße:	235 x 155 x 9 mm
Von/Mit:	Miroslav Rozlo¿ník
Erscheinungsdatum:	27.11.2018
Gewicht:	0,242 kg