Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- Part I Theoretical Foundations
- Part II Analysis of Algorithms for Phase Retrieval
- 6 Introduction to Part II
- 7 Algorithms for Phase Retrieval
- 8 The Discrete, Classical, Phase Retrieval Problem
- 9 Phase Retrieval with the Nonnegativity Constraint
- 10 Asymptotics of Hybrid Iterative Maps
- Part III Further Properties of Hybrid Iterative Algorithms and Suggestions for Improvement
- References
- Index
10 - Asymptotics of Hybrid Iterative Maps
from Part II - Analysis of Algorithms for Phase Retrieval
Published online by Cambridge University Press: 21 April 2022
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- Part I Theoretical Foundations
- Part II Analysis of Algorithms for Phase Retrieval
- 6 Introduction to Part II
- 7 Algorithms for Phase Retrieval
- 8 The Discrete, Classical, Phase Retrieval Problem
- 9 Phase Retrieval with the Nonnegativity Constraint
- 10 Asymptotics of Hybrid Iterative Maps
- Part III Further Properties of Hybrid Iterative Algorithms and Suggestions for Improvement
- References
- Index
Summary
We close this part of the book with a chapter examining the behavior of hybrid iterative maps after large numbers of iterates. The content of this chapter is rather speculative, consisting mostly of examples that illustrate various experimental phenomena. It is motivated by the observation that, except under very specific circumstances, the iterates of hybrid iterative maps do not converge. Rather, stagnation seems to occur with very high probability. The discussion in this chapter is not intended to suggest new algorithms, but rather to illustrate the extraordinary range, and beauty, of the dynamics that underlie stagnation.
- Type
- Chapter
- Information
- Geometry of the Phase Retrieval ProblemGraveyard of Algorithms, pp. 205 - 220Publisher: Cambridge University PressPrint publication year: 2022