Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-13T12:14:04.125Z Has data issue: false hasContentIssue false

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
Get access

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 Problem
Graveyard of Algorithms
, pp. 205 - 220
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×