Algorithms for Sparse Linear Systems by Jennifer Scott
Algorithms for Sparse Linear Systems - Table of Contents
- 1. Introduction to Sparse Matrices
- 2. Sparse Matrices and Their Graphs
- 3. Introduction to Matrix Factorizations
- 4. Sparse Cholesky: Symbolic Phase
- 5. Sparse Cholesky: Factorization Phase
- 6. Sparse LU Factorizations and Pivoting
- 7. Stability, Ill-Conditioning & Indefinite Systems
- 8. Sparse Matrix Ordering Algorithms
- 9. Algebraic Preconditioners & Approximations
- 10. Incomplete Factorizations (ILU / IC)
- 11. Sparse Approximate Inverse Preconditioners
- 12. Corrections and Errata
What You Will Learn in Algorithms for Sparse Linear Systems
Algorithms for Sparse Linear Systems by Jennifer Scott and Miroslav Tuma is an authoritative, mathematically rigorous textbook published by Springer that provides a modern, comprehensive treatment of direct solvers, matrix ordering techniques, and algebraic preconditioning strategies for large-scale sparse linear systems. This state-of-the-art volume guides readers through sparse matrix graph representations, symbolic Cholesky elimination trees, supernodal and multifrontal factorization phases, partial pivoting in sparse LU, stability and ill-conditioning remedies, fill-reducing reordering algorithms (AMD, METIS), incomplete LU/Cholesky factorizations, and sparse approximate inverse (SPAI) preconditioners with exceptional algorithmic clarity and numerical precision.
Designed for computational scientists, numerical analysts, high-performance computing engineers, applied mathematicians, and graduate software engineers, this foundational text bridges abstract graph-theoretic concepts directly with practical high-performance algorithm design. Scott and Tuma detail step-by-step pseudo-code formulations, fill-in elimination graphs, pivot threshold strategies, error estimation, and memory footprint management for large-scale computational simulations. Whether you are developing finite element solvers, optimizing large-scale optimization codes, or parallelizing sparse direct and iterative solvers, this book offers an indispensable roadmap.
Recognized globally as one of the most complete and contemporary references on sparse matrix computations, it stands as one of the best textbooks on sparse linear algebra algorithms and preconditioning methods. By unifying graph algorithms with stable numerical factorizations and iterative preconditioning, it serves as an essential tool for mastering sparse linear systems with confidence.
Book Details & Specifications
Title:
Algorithms for Sparse Linear Systems by Jennifer Scott
Publisher:
Birkhäuser
Year:
2023
Pages:
264
Type:
PDF
Language:
English
ISBN-10 #:
3031258193
ISBN-13 #:
978-3031258190
License:
CC BY 4.0
Amazon:
Amazon
About the Author: Jennifer Ann Scott
The author Jennifer Ann Scott
is Professor of Applied Mathematics at the University of Reading and a STFC Senior Fellow at Rutherford Appleton Laboratory, internationally renowned for her pioneering work on sparse matrix algorithms and high-performance software libraries (HSL). Miroslav Tuma is Professor of Computer Science at Charles University, Prague, widely recognized for his extensive research in sparse matrix factorizations, preconditioning techniques, and numerical linear algebra.
Through Algorithms for Sparse Linear Systems, Scott and Tuma deliver a masterfully written, state-of-the-art guide to sparse matrix computation. Their rigorous algorithmic steps, clear graph-theoretic explanations, and practical performance insights make this text a classic reference for sparse linear algebra and scientific software development trusted by researchers and engineers worldwide.
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