Algorithms for Sparse Linear Systems

This open-access monograph discusses factorization algorithms for solving large sparse linear systems, emphasizing classical techniques, approximate direct and inverse factorizations, and a unified framework for understanding sparse direct methods. It is aimed at students, computational scientists, and software developers interested in tackling sparse systems.

Format: Paperback / softback
Length: 242 pages
Publication date: 30 April 2023
Publisher: Birkhauser Verlag AG

Large sparse linear systems of equations are prevalent in science, engineering, and beyond. This open-access monograph focuses on factorization algorithms for solving such systems. It presents classical techniques for complete factorizations used in sparse direct methods and discusses the computation of approximate direct and inverse factorizations crucial for 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 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.
Sparse linear systems of equations are prevalent in various fields, including science, engineering, and beyond. This open-access monograph delves into factorization algorithms specifically designed to solve these systems. It begins by presenting classical techniques for complete factorizations, which are essential in sparse direct methods. These techniques are then discussed in the context of computing approximate direct and inverse factorizations, which play a pivotal role in constructing general-purpose algebraic preconditioners for iterative solvers.

A unified framework is employed throughout the monograph to emphasize the underlying sparsity structures and highlight the significance of understanding sparse direct methods when developing algebraic preconditioners. Theoretical results are complemented by concise outlines of sparse matrix algorithms, providing a practical perspective to the subject matter.

The target audience of this monograph includes students of applied mathematics and scientific computing, as well as computational scientists and software developers who are interested in gaining a deeper understanding of the theory and algorithms required to tackle sparse systems. It is assumed that the reader possesses a foundational knowledge in linear algebra and numerical mathematics.

By exploring the complexities of factorization algorithms and their applications in solving sparse linear systems, this monograph aims to provide valuable insights and tools for researchers and practitioners in the field. It serves as a comprehensive resource for those seeking to advance their knowledge and expertise in this area.

Weight: 409g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031258190
Edition number: 1st ed. 2023