Algorithms for Sparse Linear Systems

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Beschreibung

Large sparse linear systems of equations are ubiquitous in science, engineering and beyond. This open access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations that are used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations that are key to constructing general-purpose algebraic preconditioners for iterative solvers. A unified framework is used that emphasizes the underlying sparsity structures and highlights the importance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by sparse matrix algorithm outlines.

This monograph is aimed at students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in understanding the theory and algorithms needed to tackle sparse systems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics.

Über den Autor

¿Jennifer Scott is a Professor of Mathematics at the University of Reading and an Individual Merit Research Fellow at the Rutherford Appleton Laboratory. She is a SIAM Fellow and a Fellow of the Institute of Mathematics and its Applications. She is the author of many widely used sparse matrix packages that are available as part of the HSL Mathematical Software Library.

Miroslav Tuma is a Professor and Head of the Department of Numerical Mathematics at Charles University and was formerly a Professor at the Institute of Computer Science of the Academy of Sciences of the Czech Republic. His research has included important contributions to the development of algebraic preconditioners for iterative solvers. He was the recipient of a SIAM outstanding paper prize for his work on sparse approximate inverse preconditioners.

Zusammenfassung

This book is open access, which means that you have free and unlimited access

This monograph presents factorization algorithms for solving large sparse linear systems of equations

It unifies the study of direct methods and algebraic preconditioners that are traditionally treated separately.

Sparse matrix algorithm outlines complement theoretical results.

Inhaltsverzeichnis

An introduction to sparse matrices.- Sparse matrices and their graphs.- Introduction to matrix factorizations.- Sparse Cholesky sovler: The symbolic phase.- Sparse Cholesky solver: The factorization phase.- Sparse LU factorizations.- Stability, ill-conditioning and symmetric indefinite factorizations.- Sparse matrix ordering algorithms.- Algebraic preconditioning and approximate factorizations.- Incomplete factorizations.- Sparse approximate inverse preconditioners.

Details

Erscheinungsjahr:	2023
Fachbereich:	Wahrscheinlichkeitstheorie
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xix 242 S. 43 s/w Illustr. 27 farbige Illustr. 242 p. 70 illus. 27 illus. in color.
ISBN-13:	9783031258190
ISBN-10:	3031258193
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Scott, Jennifer T¿ma, Miroslav
Auflage:	1st edition 2023
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 15 mm
Von/Mit:	Jennifer Scott (u. a.)
Erscheinungsdatum:	30.04.2023
Gewicht:	0,406 kg

Artikel-ID: 126265661