Iterative Solution of Large Sparse Systems...

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Beschreibung

In the second edition of this classic monograph, complete with four new chapters and updated references, readers will now have access to content describing and analysing classical and modern methods with emphasis on the algebraic structure of linear iteration, which is usually ignored in other literature.

The necessary amount of work increases dramatically with the size of systems, so one has to search for algorithms that most efficiently and accurately solve systems of, e.g., several million equations. The choice of algorithms depends on the special properties the matrices in practice have. An important class of large systems arises from the discretization of partial differential equations. In this case, the matrices are sparse (i.e., they contain mostly zeroes) and well-suited to iterative algorithms.

The first edition of this book grew out of a series of lectures given by the author at the Christian-Albrecht University of Kiel to students of mathematics. The second edition includes quite novel approaches.

Über den Autor

Wolfgang Hackbusch is a Professor in the Scientific Computing department at Max Planck Institute for Mathematics in the Sciences. His research areas include numerical treatment of partial differential equations, numerical treatment of integral equations, and hierarchical matrices.

Zusammenfassung

New edition provides emphasis on the algebraic structure of linear iteration, not usually included in most literature

Completely renewed references

Content grew out of a series of lectures given by author

Extensive and useful appendices included

Includes supplementary material: [...]

Inhaltsverzeichnis

Part I: Linear Iterations.- Introduction.- Iterative Methods.- Classical Linear Iterations in the Positive Definite Case.- Analysis of Classical Iterations Under Special Structural Conditions.- Algebra of Linear Iterations.- Analysis of Positive Definite Iterations.- Generation of Iterations. Part II: Semi-Iterations and Krylov Methods.- Semi-Iterative Methods.- Gradient Methods.- Conjugate Gradient Methods and Generalizations.- Part III: Special Iterations.- Multigrid Iterations.- Domain Decomposition and Subspace Methods.- H-LU Iteration.- Tensor-based Methods.- Appendices.

Details

Erscheinungsjahr:	2018
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xxiii 509 S. 15 s/w Illustr. 11 farbige Illustr. 509 p. 26 illus. 11 illus. in color.
ISBN-13:	9783319803609
ISBN-10:	3319803603
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Hackbusch, Wolfgang
Auflage:	Softcover reprint of the original 2nd edition 2016
Hersteller:	Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 29 mm
Von/Mit:	Wolfgang Hackbusch
Erscheinungsdatum:	31.05.2018
Gewicht:	0,803 kg

Artikel-ID: 114147053