Algorithms for Sparse Linear Systems

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 sparsesystems. It is assumed that the reader has completed a basic course in linear algebra and numerical mathematics. 

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. 

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.

Autor*in

Jennifer Scott

Themen in »Algorithms for Sparse Linear Systems«

Open Access Sparse Matrices Algebraic Preconditioners Sparse Direct Methods Incomplete Factorizations Approximate Inverses

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“This book provides an admirably succinct account of direct methods for the solution of symmetric and unsymmetric linear systems of equations, including pointers to the most recent research. … it is a valuable addition to the (sparse!) collection of books on this fundamental problem in computational mathematics.” (James Andrew J. Hall, Mathematical Reviews, April, 2026)

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