Algorithms for Sparse Linear Systems

1. Auflage 2023
ISBN: 978-3-031-25819-0
Verlag: Springer International Publishing

Buch, Englisch, 242 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 406 g

Reihe: Necas Center Series

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. 

Zielgruppe

Research

Autoren/Hrsg.

Scott, Jennifer

T¿ma, Miroslav

Tuma, Miroslav

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

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.

Über Autor(innen)

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.