Applied Iterative Methods

Byrne \, Charles L.

• Part I: Preliminaries 1. Introduction 2. Background 3. BasicConcepts 4. Metric Spaces and Norms Part II: Overview 5. Operators 6. Problems and Algorithms Part III: Operators 7. Averaged and Paracontractive Operators Part IV: Algorithms 8. The Algebraic Reconstruction Technique 9. Simultaneous and Block-Iterative ART 10. Jacobi and Gauss-Seidel Methods 11. Conjugate-Direction Methods in Optimization Part V: Positivity in Linear Systems 12. The Multiplicative ART (MART) 13. Rescaled Block-Iterative (RBI) Methods Part VI: Stability 14. Sensitivity to Noise 15. Feedback in Block-Iterative Reconstruction Part VII: Optimization 16. Iterative Optimization 17. Convex Sets and Convex Functions 18. Generalized Projections onto Convex Sets 19. The Split Feasibility Problem 20. Nonsmooth Optimization 21. An Interior-Point Optimization Method 22. Linear and Convex Programming 23. Systems of Linear Inequalities 24. Constrained Iteration Methods 25. Fourier Transform Estimation Part VIII: Applications 26. Tomography 27. Intensity-Modulated Radiation Therapy 28. Magnetic-Resonance Imaging 29. Hyperspectral Imaging 30. Planewave Propagation 31. Inverse Problems and the Laplace Transform 32. Detection and Classification

" ""... written for scientists and engineers, and mostly concerned with operators on finite-dimensional Euclidean space."" -SciTech Book News, March 2008With an emphasis on the technique's broad spectrum of practical applications, Charles Byrne's Applied Iterative Methods provides a thorough treatment of the iterative approach, one of the most fundamental processes used in numerical analysis. ... Unique in its cohesive treatment of a diverse array of algorithms, this book serves as a self-contained guide for those interested in exploring the many applications ofthis technique. -L'Enseignement Mathematique, August 2008This book gives an overview of [inverse] problems and techniques for the solution of industrial inverse problems arising in acoustic signal processing, optical imaging and medical tomography. Byrne has made significant contributions to this area for some time, and many of these important results are collected in this book. The methods are analyzed on a sound mathematical functional analytical basis. . . . The book can be used as a text for a graduate-level course on interative methods for linear systems for mathematicians, computer scientists or engineers. The presentation is very clear. -Maxim Larin, Mathematiacl Reviews, August 2008"