Applied & Computational Linear Algebra by Charles Byrne
Applied & Computational Linear Algebra - Table of Contents
Part-I Preliminaries
1. Introduction
2. An Overview of Applications
3. A Little Matrix Theory
4. The ART, MART and EM-MART
Part-II Algebra
5. More Matrix Theory
6. Metric Spaces and Norms
7. Under-Determined Systems of Linear Equations
8. Convex Sets
9. Linear Inequalities
Part-III Algorithms
10. Fixed-Point Methods
11. Jacobi and Gauss-Seidel Methods
12. A Tale of Two Algorithms
13. Block-Iterative Methods I
14. The Split Feasibility Problem
15. Conjugate-Direction Methods
16. Regularization
17. Transmission Tomography I
18. Transmission Tomography II
19. Emission Tomography
20. Magnetic Resonance Imaging
21. Intensity Modulated Radiation Therapy
22. Appendix: Linear Algebra
23. Appendix: Even More Matrix Theory
24. Appendix: More ART and MART
25. Appendix: Constrained Iteration Methods
26. Appendix: Block-Iterative Methods II
27. Appendix: Eigenvalue Bounds
28. Appendix: List-Mode Reconstruction in PET
29. Appendix: A Little Optimization
30. Appendix: Geometric Programming and the MART
31. Appendix: Fourier Transforms and the FFT
32. Appendix: Hermitian and Normal Linear Operators
33. Appendix: Sturm-Liouville Problems
34. Appendix: Hermite’s Equations and Quantum Mechanics
35. Appendix: The BLUE and The Kalman Filter
36. Appendix: Matrix and Vector Differentiation
37. Appendix: Signal Detection and Estimation
What You Will Learn in Applied & Computational Linear Algebra
"Applied & Computational Linear Algebra: A First Course" by Charles L. Byrne is a practical and application-focused guide to modern linear algebra, designed for students who want to connect theory with real computation. The book emphasizes "linear systems", "matrix algorithms", "numerical computation", "iterative methods", and "applied mathematics", making it highly relevant for today’s data-driven fields.
Rather than treating linear algebra as a purely abstract subject, Byrne presents concepts through real computational problems. Readers learn how vectors, matrices, and transformations are used to solve large-scale systems, least squares problems, and optimization tasks. The text explains not only the mathematics behind these methods but also why certain algorithms work better in practical computing environments.
A major strength of the book is its clear focus on implementation and efficiency. Many examples are drawn from scientific computing, signal processing, and imaging applications, helping readers see how linear algebra supports modern technology. With its balanced approach to theory and computation, the book is well suited for applied mathematics, engineering, and computer science students who want both understanding and practical skills.
Book Details & Specifications
Title:
Applied & Computational Linear Algebra by Charles Byrne
Publisher:
University of Massachusetts Lowell
Year:
2013
Pages:
504
Type:
PDF
Language:
English
ISBN-10 #:
3319403397
ISBN-13 #:
978-3319403397
License:
External Educational Resource
Amazon:
Amazon
About the Author: Charles L. Byrne
The author Charles L. Byrne
is a mathematician and is professor at Department of Mathematical Sciences, University of Massachusetts Lowell, Lowell, Massachusetts, United States. He is known for his work in "applied linear algebra", "computational mathematics", and "numerical analysis". He focused on connecting mathematical theory with practical problem-solving. His teaching emphasizes clarity, intuition, and real-world relevance. Byrne’s research centers on "iterative algorithms", "optimization", and "inverse problems", with applications in image reconstruction and scientific computing. As an author, he is valued for making complex mathematical ideas accessible to students and professionals, helping learners understand how linear algebra supports modern computational and engineering applications.
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