Applied & Computational Linear Algebra by Charles Byrne
Applied & Computational Linear Algebra - Table of Contents
PART I & II: PRELIMINARIES & ALGEBRA
- 1. Introduction
- 2. An Overview of Applications
- 3. A Little Matrix Theory
- 4. The ART, MART and EM-MART
- 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 & IMAGING
- 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 Techniques
- 17. Transmission Tomography I
- 18. Transmission Tomography II
- 19. Emission Tomography
- 20. Magnetic Resonance Imaging
- 21. Intensity Modulated Radiation Therapy
PART IV: MATHEMATICAL APPENDICES
- 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 by Charles Byrne is an authoritative, mathematically rigorous monograph published by A K Peters/CRC Press that demonstrates how numerical linear algebra, convex optimization, and operator theory solve real-world inverse problems in medical imaging and signal processing. This comprehensive volume guides readers through matrix theory, metric space norms, under-determined linear systems, convex inequalities, Jacobi and Gauss-Seidel iterations, conjugate-direction methods, Tikhonov regularization, and tomographic image reconstruction models (transmission, emission, MRI, and IMRT) with exceptional analytical precision and structural logic.
Designed for graduate students, computational mathematicians, biomedical engineers, medical physicists, and signal processing researchers, this foundational text bridges pure functional analysis and practical inverse algorithms. Byrne details step-by-step formulations for the Algebraic Reconstruction Technique (ART), Multiplicative ART (MART), split feasibility problems, and Poisson likelihood maximization in PET/SPECT imaging. Whether you are developing CT image reconstruction kernels, analyzing convergence rates of block-iterative methods, or studying Kalman filtering in signal estimation, this book offers an indispensable roadmap.
Recognized globally as a definitive treatise on the linear algebra of inverse problems, it stands as one of the best computational linear algebra books for self-study. By connecting abstract operator theory directly to medical imaging software systems, it serves as an essential tool for mastering applied matrix algorithms and imaging mathematics with confidence.
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 Professor Emeritus of Mathematics at the University of Massachusetts Lowell, internationally recognized for his pioneering contributions to iterative optimization algorithms, image reconstruction in medical tomography, and signal estimation. He has authored multiple seminal books on optimization, functional analysis, and mathematical methods for inverse problems.
Through Applied & Computational Linear Algebra, Byrne brings decades of specialized research in tomographic algorithms directly into a structured pedagogical format. His clear proof structures, deep emphasis on real-world application, and comprehensive mathematical appendices make this volume a classic reference for computational linear algebra and image processing trusted by applied mathematicians and imaging scientists worldwide.
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