國立高雄大學圖資館 |

Language: English

Back

Algorithms for sparse linear systems

Record Type:	Electronic resources : Monograph/item
Title/Author:	Algorithms for sparse linear systemsby Jennifer Scott, Miroslav Tůma.
Author:	Scott, Jennifer.
other author:	Tůma, Miroslav.
Published:	Cham :Springer International Publishing :2023.
Description:	xix, 242 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Sparse matrices.
Online resource:	https://doi.org/10.1007/978-3-031-25820-6
ISBN:	9783031258206$q(electronic bk.)

Algorithms for sparse linear systems
Scott, Jennifer.

Algorithms for sparse linear systems[electronic resource] /by Jennifer Scott, Miroslav Tůma. - Cham :Springer International Publishing :2023. - xix, 242 p. :ill. (some col.), digital ;24 cm. - Necas center series,2523-3351. - Necas center series..

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.

Open access.

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.

ISBN: 9783031258206$q(electronic bk.)

Standard No.: 10.1007/978-3-031-25820-6doiSubjects--Topical Terms:

211248
Sparse matrices.

LC Class. No.: QA188

Dewey Class. No.: 512.9434

Algorithms for sparse linear systems
LDR:02602nmm a2200349 a 4500 001 643386
003 DE-He213
005 20230429200329.0
006 m d
007 cr nn 008maaau
008 231123s2023 sz s 0 eng d
020 $a 9783031258206$q(electronic bk.)
020 $a 9783031258190$q(paper)
024 7 $a 10.1007/978-3-031-25820-6 $2 doi
035 $a 978-3-031-25820-6
040 $a GP $c GP
041 0 $a eng
050 4 $a QA188
072 7 $a PBKS $2 bicssc
072 7 $a MAT021000 $2 bisacsh
072 7 $a PBKS $2 thema
082 0 4 $a 512.9434 $2 23
090 $a QA188 $b .S427 2023
100 1 $a Scott, Jennifer. $3 951102
245 1 0 $a Algorithms for sparse linear systems $h [electronic resource] / $c by Jennifer Scott, Miroslav Tůma.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhäuser, $c 2023.
300 $a xix, 242 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a Necas center series, $x 2523-3351
505 0 $a 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.
506 $a Open access.
520 $a 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.
650 0 $a Sparse matrices. $3 211248
650 0 $a Linear systems. $3 182249
650 0 $a Algorithms. $3 184661
650 1 4 $a Numerical Analysis. $3 275681
650 2 4 $a Linear Algebra. $3 821215
650 2 4 $a Computational Science and Engineering. $3 274685
700 1 $a Tůma, Miroslav. $3 951103
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Necas center series. $3 823444
856 4 0 $u https://doi.org/10.1007/978-3-031-25820-6
950 $a Mathematics and Statistics (SpringerNature-11649)