Adaptive multiresolution analysis based on anisotropic triangulations

A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function f (\mathcal {D}_j)_{j\geq 0} on these triangulations. The refinement procedure consists in bisecting a triangle T and its piecewise polynomial approximation after T norm o...

Full description

Saved in:
Bibliographic Details
Published in:Mathematics of computation 2012-04, Vol.81 (278), p.789-810
Main Authors: COHEN, ALBERT, DYN, NIRA, HECHT, FRÉDÉRIC, MIREBEAU, JEAN-MARIE
Format: Article
Language:English
Subjects:
Approximation
Aspect ratio
Computer Science
Degrees of polynomials
Image compression
Mathematical functions
Mathematics
Numerical Analysis
Polynomials
Triangles
Triangulation
Vertices
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-a405t-e780da691f11a23dd161e3e41f5c07f54785b6391e3214679500eeddce692663
cites
container_end_page 810
container_issue 278
container_start_page 789
container_title Mathematics of computation
container_volume 81
creator COHEN, ALBERT
DYN, NIRA
HECHT, FRÉDÉRIC
MIREBEAU, JEAN-MARIE
description A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function f (\mathcal {D}_j)_{j\geq 0} on these triangulations. The refinement procedure consists in bisecting a triangle T and its piecewise polynomial approximation after T norm of all these approximations. Numerical tests performed in the case of piecewise linear approximation of functions with analytic expressions or of numerical images illustrate the fact that the refinement procedure generates triangles with an optimal aspect ratio (which is dictated by the local Hessian of f functions).
doi_str_mv 10.1090/S0025-5718-2011-02495-6
format article
fullrecord <record><control><sourceid>jstor_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_00387804v2</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><jstor_id>23267973</jstor_id><sourcerecordid>23267973</sourcerecordid><originalsourceid>FETCH-LOGICAL-a405t-e780da691f11a23dd161e3e41f5c07f54785b6391e3214679500eeddce692663</originalsourceid><addsrcrecordid>eNqNkE9Lw0AQxRdRsFY_gpirh9WZzf7LsZRqhYIHe1-22Y1uSZuymxb67U0aydnTwJv33gw_Qp4QXhAKeP0CYIIKhZoyQKTAeCGovCITBK2p1Jxdk8louiV3KW0BAKVQE7KYOXtow8lnu2PdhuhTUx_b0Owzu7f1OYWUbWzyLrsoITVtbA6hzNoY7P77WNvem-7JTWXr5B_-5pSs3xbr-ZKuPt8_5rMVtRxES73S4KwssEK0LHcOJfrcc6xECaoSXGmxkXnRiQy5VIUA8N650suCSZlPyfNQ-2Nrc4hhZ-PZNDaY5Wxleg0g190NfmKdVw3eMjYpRV-NAQTTgzMXcKZnYnpw5gLO9Fceh-Q2tU0cYyxn3Ucq7_Zs2Ntd-nfpLzu_eSI</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Adaptive multiresolution analysis based on anisotropic triangulations</title><source>JSTOR Archival Journals and Primary Sources Collection</source><source>American Mathematical Society Publications (Freely Accessible)</source><creator>COHEN, ALBERT ; DYN, NIRA ; HECHT, FRÉDÉRIC ; MIREBEAU, JEAN-MARIE</creator><creatorcontrib>COHEN, ALBERT ; DYN, NIRA ; HECHT, FRÉDÉRIC ; MIREBEAU, JEAN-MARIE</creatorcontrib><description>A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function f (\mathcal {D}_j)_{j\geq 0} on these triangulations. The refinement procedure consists in bisecting a triangle T and its piecewise polynomial approximation after T norm of all these approximations. Numerical tests performed in the case of piecewise linear approximation of functions with analytic expressions or of numerical images illustrate the fact that the refinement procedure generates triangles with an optimal aspect ratio (which is dictated by the local Hessian of f functions).</description><identifier>ISSN: 0025-5718</identifier><identifier>EISSN: 1088-6842</identifier><identifier>DOI: 10.1090/S0025-5718-2011-02495-6</identifier><language>eng</language><publisher>American Mathematical Society</publisher><subject>Approximation ; Aspect ratio ; Computer Science ; Degrees of polynomials ; Image compression ; Mathematical functions ; Mathematics ; Numerical Analysis ; Polynomials ; Triangles ; Triangulation ; Vertices</subject><ispartof>Mathematics of computation, 2012-04, Vol.81 (278), p.789-810</ispartof><rights>Copyright 2011, American Mathematical Society</rights><rights>2012 American Mathematical Society</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-a405t-e780da691f11a23dd161e3e41f5c07f54785b6391e3214679500eeddce692663</citedby><orcidid>0000-0002-7356-0872 ; 0000-0003-1337-4012</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttp://www.ams.org/mcom/2012-81-278/S0025-5718-2011-02495-6/S0025-5718-2011-02495-6.pdf$$EPDF$$P50$$Gams$$H</linktopdf><linktohtml>$$Uhttp://www.ams.org/mcom/2012-81-278/S0025-5718-2011-02495-6/$$EHTML$$P50$$Gams$$H</linktohtml><link.rule.ids>69,230,314,780,784,885,23324,27924,27925,58238,58471,77838,77848</link.rule.ids><backlink>$$Uhttps://hal.science/hal-00387804$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>COHEN, ALBERT</creatorcontrib><creatorcontrib>DYN, NIRA</creatorcontrib><creatorcontrib>HECHT, FRÉDÉRIC</creatorcontrib><creatorcontrib>MIREBEAU, JEAN-MARIE</creatorcontrib><title>Adaptive multiresolution analysis based on anisotropic triangulations</title><title>Mathematics of computation</title><description>A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function f (\mathcal {D}_j)_{j\geq 0} on these triangulations. The refinement procedure consists in bisecting a triangle T and its piecewise polynomial approximation after T norm of all these approximations. Numerical tests performed in the case of piecewise linear approximation of functions with analytic expressions or of numerical images illustrate the fact that the refinement procedure generates triangles with an optimal aspect ratio (which is dictated by the local Hessian of f functions).</description><subject>Approximation</subject><subject>Aspect ratio</subject><subject>Computer Science</subject><subject>Degrees of polynomials</subject><subject>Image compression</subject><subject>Mathematical functions</subject><subject>Mathematics</subject><subject>Numerical Analysis</subject><subject>Polynomials</subject><subject>Triangles</subject><subject>Triangulation</subject><subject>Vertices</subject><issn>0025-5718</issn><issn>1088-6842</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNqNkE9Lw0AQxRdRsFY_gpirh9WZzf7LsZRqhYIHe1-22Y1uSZuymxb67U0aydnTwJv33gw_Qp4QXhAKeP0CYIIKhZoyQKTAeCGovCITBK2p1Jxdk8louiV3KW0BAKVQE7KYOXtow8lnu2PdhuhTUx_b0Owzu7f1OYWUbWzyLrsoITVtbA6hzNoY7P77WNvem-7JTWXr5B_-5pSs3xbr-ZKuPt8_5rMVtRxES73S4KwssEK0LHcOJfrcc6xECaoSXGmxkXnRiQy5VIUA8N650suCSZlPyfNQ-2Nrc4hhZ-PZNDaY5Wxleg0g190NfmKdVw3eMjYpRV-NAQTTgzMXcKZnYnpw5gLO9Fceh-Q2tU0cYyxn3Ucq7_Zs2Ntd-nfpLzu_eSI</recordid><startdate>20120401</startdate><enddate>20120401</enddate><creator>COHEN, ALBERT</creator><creator>DYN, NIRA</creator><creator>HECHT, FRÉDÉRIC</creator><creator>MIREBEAU, JEAN-MARIE</creator><general>American Mathematical Society</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope><orcidid>https://orcid.org/0000-0002-7356-0872</orcidid><orcidid>https://orcid.org/0000-0003-1337-4012</orcidid></search><sort><creationdate>20120401</creationdate><title>Adaptive multiresolution analysis based on anisotropic triangulations</title><author>COHEN, ALBERT ; DYN, NIRA ; HECHT, FRÉDÉRIC ; MIREBEAU, JEAN-MARIE</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a405t-e780da691f11a23dd161e3e41f5c07f54785b6391e3214679500eeddce692663</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>Approximation</topic><topic>Aspect ratio</topic><topic>Computer Science</topic><topic>Degrees of polynomials</topic><topic>Image compression</topic><topic>Mathematical functions</topic><topic>Mathematics</topic><topic>Numerical Analysis</topic><topic>Polynomials</topic><topic>Triangles</topic><topic>Triangulation</topic><topic>Vertices</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>COHEN, ALBERT</creatorcontrib><creatorcontrib>DYN, NIRA</creatorcontrib><creatorcontrib>HECHT, FRÉDÉRIC</creatorcontrib><creatorcontrib>MIREBEAU, JEAN-MARIE</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Mathematics of computation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>COHEN, ALBERT</au><au>DYN, NIRA</au><au>HECHT, FRÉDÉRIC</au><au>MIREBEAU, JEAN-MARIE</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Adaptive multiresolution analysis based on anisotropic triangulations</atitle><jtitle>Mathematics of computation</jtitle><date>2012-04-01</date><risdate>2012</risdate><volume>81</volume><issue>278</issue><spage>789</spage><epage>810</epage><pages>789-810</pages><issn>0025-5718</issn><eissn>1088-6842</eissn><abstract>A simple greedy refinement procedure for the generation of data-adapted triangulations is proposed and studied. Given a function f (\mathcal {D}_j)_{j\geq 0} on these triangulations. The refinement procedure consists in bisecting a triangle T and its piecewise polynomial approximation after T norm of all these approximations. Numerical tests performed in the case of piecewise linear approximation of functions with analytic expressions or of numerical images illustrate the fact that the refinement procedure generates triangles with an optimal aspect ratio (which is dictated by the local Hessian of f functions).</abstract><pub>American Mathematical Society</pub><doi>10.1090/S0025-5718-2011-02495-6</doi><tpages>22</tpages><orcidid>https://orcid.org/0000-0002-7356-0872</orcidid><orcidid>https://orcid.org/0000-0003-1337-4012</orcidid><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0025-5718
ispartof Mathematics of computation, 2012-04, Vol.81 (278), p.789-810
issn 0025-5718
1088-6842
language eng
recordid cdi_hal_primary_oai_HAL_hal_00387804v2
source JSTOR Archival Journals and Primary Sources Collection; American Mathematical Society Publications (Freely Accessible)
subjects Approximation
Aspect ratio
Computer Science
Degrees of polynomials
Image compression
Mathematical functions
Mathematics
Numerical Analysis
Polynomials
Triangles
Triangulation
Vertices
title Adaptive multiresolution analysis based on anisotropic triangulations
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T05%3A32%3A44IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-jstor_hal_p&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Adaptive%20multiresolution%20analysis%20based%20on%20anisotropic%20triangulations&rft.jtitle=Mathematics%20of%20computation&rft.au=COHEN,%20ALBERT&rft.date=2012-04-01&rft.volume=81&rft.issue=278&rft.spage=789&rft.epage=810&rft.pages=789-810&rft.issn=0025-5718&rft.eissn=1088-6842&rft_id=info:doi/10.1090/S0025-5718-2011-02495-6&rft_dat=%3Cjstor_hal_p%3E23267973%3C/jstor_hal_p%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-a405t-e780da691f11a23dd161e3e41f5c07f54785b6391e3214679500eeddce692663%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=23267973&rfr_iscdi=true