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Open access
Title
Algorithms for sparse linear systems / Jennifer Scott, Miroslav Tůma.
ISBN
9783031258206 electronic book
3031258207 electronic book
9783031258190
Published
Cham : Birkhäuser, 2023.
Language
English
Description
1 online resource (xix, 242 pages) : illustrations (some color).
Item Number
10.1007/978-3-031-25820-6 doi
Call Number
QA188 .S36 2023
Dewey Decimal Classification
512.9/434
Summary
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.
Access Note
Open access.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed May 3, 2023).
Series
Nečas Center series, 2523-3351
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.
