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10 - Asymptotics of Hybrid Iterative Maps

from Part II - Analysis of Algorithms for Phase Retrieval

Published online by Cambridge University Press:  21 April 2022

Alexander H. Barnett
Affiliation:
Flatiron Institute
Charles L. Epstein
Affiliation:
Flatiron Institute
Leslie Greengard
Affiliation:
Courant Institute
Jeremy Magland
Affiliation:
Flatiron Institute
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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.

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Chapter
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Geometry of the Phase Retrieval Problem
Graveyard of Algorithms
, pp. 205 - 220
Publisher: Cambridge University Press
Print publication year: 2022

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