A global approach to the refinement of manifold data

A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and approximation of manifold-valued functions by repeated refineme...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics of computation 2017-01, Vol.86 (303), p.375-395
Main Authors: DYN, NIRA, SHARON, NIR
Format: Article
Language:English
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-a326t-2f05c067a187633dad8f3d41d5a62392f84b0e23be5bb899aa66c1cf7b4156e03
cites
container_end_page 395
container_issue 303
container_start_page 375
container_title Mathematics of computation
container_volume 86
creator DYN, NIRA
SHARON, NIR
description A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and approximation of manifold-valued functions by repeated refinements schemes. Most refinement methods compute each refined element separately, independently of the computations of the other elements. Here we propose a global method which computes all the refined elements simultaneously, using geodesic averages. We analyse repeated refinements schemes based on this global approach, and derive conditions guaranteeing strong convergence.
doi_str_mv 10.1090/mcom/3087
format article
fullrecord <record><control><sourceid>jstor_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1090_mcom_3087</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>mathcomp.86.303.375</jstor_id><sourcerecordid>mathcomp.86.303.375</sourcerecordid><originalsourceid>FETCH-LOGICAL-a326t-2f05c067a187633dad8f3d41d5a62392f84b0e23be5bb899aa66c1cf7b4156e03</originalsourceid><addsrcrecordid>eNp9zztPwzAUhmELgUQpDPwDDwwwhB7b8SVjVXGTKrHAbJ0kNkkV11HshX9PoiJGprM8-nReQm4ZPDKoYBOaGDYCjD4jKwbGFMqU_JysALgspGbmklyldAAApqRekXJLv4ZY40BxHKeITUdzpLlzdHK-P7rgjplGTwMeex-HlraY8ZpceBySu_m9a_L5_PSxey327y9vu-2-QMFVLrgH2YDSyIxWQrTYGi_akrUSFRcV96aswXFRO1nXpqoQlWpY43VdMqkciDV5OO02U0xpfsiOUx9w-rYM7JJrl1y75M72_mQPKcfpDwbM3WxGa9TshBVazvTuRDGkfxZ_AIcSYWU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>A global approach to the refinement of manifold data</title><source>JSTOR Archival Journals and Primary Sources Collection</source><source>American Mathematical Society Publications (Freely Accessible)</source><creator>DYN, NIRA ; SHARON, NIR</creator><creatorcontrib>DYN, NIRA ; SHARON, NIR</creatorcontrib><description>A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and approximation of manifold-valued functions by repeated refinements schemes. Most refinement methods compute each refined element separately, independently of the computations of the other elements. Here we propose a global method which computes all the refined elements simultaneously, using geodesic averages. We analyse repeated refinements schemes based on this global approach, and derive conditions guaranteeing strong convergence.</description><identifier>ISSN: 0025-5718</identifier><identifier>EISSN: 1088-6842</identifier><identifier>DOI: 10.1090/mcom/3087</identifier><language>eng</language><publisher>American Mathematical Society</publisher><ispartof>Mathematics of computation, 2017-01, Vol.86 (303), p.375-395</ispartof><rights>Copyright 2016, American Mathematical Society</rights><rights>2016 American Mathematical Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a326t-2f05c067a187633dad8f3d41d5a62392f84b0e23be5bb899aa66c1cf7b4156e03</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttp://www.ams.org/mcom/2017-86-303/S0025-5718-2016-03087-2/S0025-5718-2016-03087-2.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttp://www.ams.org/mcom/2017-86-303/S0025-5718-2016-03087-2/$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>69,314,776,780,23305,27903,27904,58216,58449,77584,77594</link.rule.ids></links><search><creatorcontrib>DYN, NIRA</creatorcontrib><creatorcontrib>SHARON, NIR</creatorcontrib><title>A global approach to the refinement of manifold data</title><title>Mathematics of computation</title><description>A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and approximation of manifold-valued functions by repeated refinements schemes. Most refinement methods compute each refined element separately, independently of the computations of the other elements. Here we propose a global method which computes all the refined elements simultaneously, using geodesic averages. We analyse repeated refinements schemes based on this global approach, and derive conditions guaranteeing strong convergence.</description><issn>0025-5718</issn><issn>1088-6842</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9zztPwzAUhmELgUQpDPwDDwwwhB7b8SVjVXGTKrHAbJ0kNkkV11HshX9PoiJGprM8-nReQm4ZPDKoYBOaGDYCjD4jKwbGFMqU_JysALgspGbmklyldAAApqRekXJLv4ZY40BxHKeITUdzpLlzdHK-P7rgjplGTwMeex-HlraY8ZpceBySu_m9a_L5_PSxey327y9vu-2-QMFVLrgH2YDSyIxWQrTYGi_akrUSFRcV96aswXFRO1nXpqoQlWpY43VdMqkciDV5OO02U0xpfsiOUx9w-rYM7JJrl1y75M72_mQPKcfpDwbM3WxGa9TshBVazvTuRDGkfxZ_AIcSYWU</recordid><startdate>20170101</startdate><enddate>20170101</enddate><creator>DYN, NIRA</creator><creator>SHARON, NIR</creator><general>American Mathematical Society</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170101</creationdate><title>A global approach to the refinement of manifold data</title><author>DYN, NIRA ; SHARON, NIR</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a326t-2f05c067a187633dad8f3d41d5a62392f84b0e23be5bb899aa66c1cf7b4156e03</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>DYN, NIRA</creatorcontrib><creatorcontrib>SHARON, NIR</creatorcontrib><collection>CrossRef</collection><jtitle>Mathematics of computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>DYN, NIRA</au><au>SHARON, NIR</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A global approach to the refinement of manifold data</atitle><jtitle>Mathematics of computation</jtitle><date>2017-01-01</date><risdate>2017</risdate><volume>86</volume><issue>303</issue><spage>375</spage><epage>395</epage><pages>375-395</pages><issn>0025-5718</issn><eissn>1088-6842</eissn><abstract>A refinement of manifold data is a computational process, which produces a denser set of discrete data from a given one. Such refinements are closely related to multiresolution representations of manifold data by pyramid transforms, and approximation of manifold-valued functions by repeated refinements schemes. Most refinement methods compute each refined element separately, independently of the computations of the other elements. Here we propose a global method which computes all the refined elements simultaneously, using geodesic averages. We analyse repeated refinements schemes based on this global approach, and derive conditions guaranteeing strong convergence.</abstract><pub>American Mathematical Society</pub><doi>10.1090/mcom/3087</doi><tpages>21</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0025-5718
ispartof Mathematics of computation, 2017-01, Vol.86 (303), p.375-395
issn 0025-5718
1088-6842
language eng
recordid cdi_crossref_primary_10_1090_mcom_3087
source JSTOR Archival Journals and Primary Sources Collection; American Mathematical Society Publications (Freely Accessible)
title A global approach to the refinement of manifold data
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-27T22%3A55%3A00IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20global%20approach%20to%20the%20refinement%20of%20manifold%20data&rft.jtitle=Mathematics%20of%20computation&rft.au=DYN,%20NIRA&rft.date=2017-01-01&rft.volume=86&rft.issue=303&rft.spage=375&rft.epage=395&rft.pages=375-395&rft.issn=0025-5718&rft.eissn=1088-6842&rft_id=info:doi/10.1090/mcom/3087&rft_dat=%3Cjstor_cross%3Emathcomp.86.303.375%3C/jstor_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a326t-2f05c067a187633dad8f3d41d5a62392f84b0e23be5bb899aa66c1cf7b4156e03%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rft_jstor_id=mathcomp.86.303.375&rfr_iscdi=true