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Hybrid hyperinterpolation over general regions
We present an ℓ 2 2 + ℓ 1 -regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybrid hyperinterpolation, using a soft thresholding operator and a filter function to shrink the Fourier coefficients approximat...
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Published in: | Calcolo 2025-03, Vol.62 (1), Article 3 |
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creator | An, Congpei Ran, Jiashu Sommariva, Alvise |
description | We present an
ℓ
2
2
+
ℓ
1
-regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybrid hyperinterpolation, using a soft thresholding operator and a filter function to shrink the Fourier coefficients approximated by a high-order quadrature rule of a given continuous function with respect to some orthonormal basis, is a combination of Lasso and filtered hyperinterpolations. Hybrid hyperinterpolation inherits features of them to deal with noisy data once the regularization parameter and the filter function are well chosen. We derive
L
2
errors in theoretical analysis for hybrid hyperinterpolation to approximate continuous functions with noise data on sampling points. Numerical examples illustrate the theoretical results and show that well chosen regularization parameters can enhance the approximation quality over the unit-sphere and the union of disks. |
doi_str_mv | 10.1007/s10092-024-00625-w |
format | article |
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ℓ
2
2
+
ℓ
1
-regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybrid hyperinterpolation, using a soft thresholding operator and a filter function to shrink the Fourier coefficients approximated by a high-order quadrature rule of a given continuous function with respect to some orthonormal basis, is a combination of Lasso and filtered hyperinterpolations. Hybrid hyperinterpolation inherits features of them to deal with noisy data once the regularization parameter and the filter function are well chosen. We derive
L
2
errors in theoretical analysis for hybrid hyperinterpolation to approximate continuous functions with noise data on sampling points. Numerical examples illustrate the theoretical results and show that well chosen regularization parameters can enhance the approximation quality over the unit-sphere and the union of disks.</description><identifier>ISSN: 0008-0624</identifier><identifier>EISSN: 1126-5434</identifier><identifier>DOI: 10.1007/s10092-024-00625-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Approximation ; Continuity (mathematics) ; Mathematics ; Mathematics and Statistics ; Numerical Analysis ; Operators (mathematics) ; Parameters ; Quadratures ; Regularization ; Theory of Computation</subject><ispartof>Calcolo, 2025-03, Vol.62 (1), Article 3</ispartof><rights>The Author(s) under exclusive licence to Istituto di Informatica e Telematica (IIT) 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-e67bcf42939d548530ce89804927286f0e125456d78a6c9191f3bce4421a92773</cites><orcidid>0000-0002-8902-8063</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>An, Congpei</creatorcontrib><creatorcontrib>Ran, Jiashu</creatorcontrib><creatorcontrib>Sommariva, Alvise</creatorcontrib><title>Hybrid hyperinterpolation over general regions</title><title>Calcolo</title><addtitle>Calcolo</addtitle><description>We present an
ℓ
2
2
+
ℓ
1
-regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybrid hyperinterpolation, using a soft thresholding operator and a filter function to shrink the Fourier coefficients approximated by a high-order quadrature rule of a given continuous function with respect to some orthonormal basis, is a combination of Lasso and filtered hyperinterpolations. Hybrid hyperinterpolation inherits features of them to deal with noisy data once the regularization parameter and the filter function are well chosen. We derive
L
2
errors in theoretical analysis for hybrid hyperinterpolation to approximate continuous functions with noise data on sampling points. Numerical examples illustrate the theoretical results and show that well chosen regularization parameters can enhance the approximation quality over the unit-sphere and the union of disks.</description><subject>Approximation</subject><subject>Continuity (mathematics)</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Numerical Analysis</subject><subject>Operators (mathematics)</subject><subject>Parameters</subject><subject>Quadratures</subject><subject>Regularization</subject><subject>Theory of Computation</subject><issn>0008-0624</issn><issn>1126-5434</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2025</creationdate><recordtype>article</recordtype><recordid>eNp9kEFPwzAMhSMEEmPwBzhV4pzhOGnaHNEEDGkSFzhHXeuWTqMtTse0f0-gSNy42LL93rP0CXGtYKEAstsQq0MJaCSAxVQeTsRMKbQyNdqcihkA5DJezLm4CGEbx9TkZiYWq-OG2yp5Ow7EbTcSD_2uGNu-S_pP4qShjrjYJUxN3IVLcVYXu0BXv30uXh_uX5YruX5-fFrerWWJAKMkm23K2qDTrop_Ug0l5S4H4zDD3NZAClOT2irLC1s65VStNyUZg6qIkkzPxc2UO3D_sacw-m2_5y6-9Fppo9HqDKMKJ1XJfQhMtR-4fS_46BX4by5-4uIjF__DxR-iSU-mEMVdQ_wX_Y_rCxgzZEs</recordid><startdate>20250301</startdate><enddate>20250301</enddate><creator>An, Congpei</creator><creator>Ran, Jiashu</creator><creator>Sommariva, Alvise</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-8902-8063</orcidid></search><sort><creationdate>20250301</creationdate><title>Hybrid hyperinterpolation over general regions</title><author>An, Congpei ; Ran, Jiashu ; Sommariva, Alvise</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-e67bcf42939d548530ce89804927286f0e125456d78a6c9191f3bce4421a92773</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2025</creationdate><topic>Approximation</topic><topic>Continuity (mathematics)</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Numerical Analysis</topic><topic>Operators (mathematics)</topic><topic>Parameters</topic><topic>Quadratures</topic><topic>Regularization</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>An, Congpei</creatorcontrib><creatorcontrib>Ran, Jiashu</creatorcontrib><creatorcontrib>Sommariva, Alvise</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Calcolo</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>An, Congpei</au><au>Ran, Jiashu</au><au>Sommariva, Alvise</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Hybrid hyperinterpolation over general regions</atitle><jtitle>Calcolo</jtitle><stitle>Calcolo</stitle><date>2025-03-01</date><risdate>2025</risdate><volume>62</volume><issue>1</issue><artnum>3</artnum><issn>0008-0624</issn><eissn>1126-5434</eissn><abstract>We present an
ℓ
2
2
+
ℓ
1
-regularized discrete least squares approximation over general regions under assumptions of hyperinterpolation, named hybrid hyperinterpolation. Hybrid hyperinterpolation, using a soft thresholding operator and a filter function to shrink the Fourier coefficients approximated by a high-order quadrature rule of a given continuous function with respect to some orthonormal basis, is a combination of Lasso and filtered hyperinterpolations. Hybrid hyperinterpolation inherits features of them to deal with noisy data once the regularization parameter and the filter function are well chosen. We derive
L
2
errors in theoretical analysis for hybrid hyperinterpolation to approximate continuous functions with noise data on sampling points. Numerical examples illustrate the theoretical results and show that well chosen regularization parameters can enhance the approximation quality over the unit-sphere and the union of disks.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s10092-024-00625-w</doi><orcidid>https://orcid.org/0000-0002-8902-8063</orcidid></addata></record> |
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language | eng |
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subjects | Approximation Continuity (mathematics) Mathematics Mathematics and Statistics Numerical Analysis Operators (mathematics) Parameters Quadratures Regularization Theory of Computation |
title | Hybrid hyperinterpolation over general regions |
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