{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,11]],"date-time":"2025-12-11T07:39:39Z","timestamp":1765438779727},"reference-count":27,"publisher":"Walter de Gruyter GmbH","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,4,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper is concerned with the use of the focal underdetermined system solver to recover sparse empirical quadrature rules for parametrized integrals from existing data. This algorithm, originally proposed for image and signal reconstruction, relies on an approximated <jats:inline-formula id=\"j_cmam-2021-0131_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi mathvariant=\"normal\">\u2113<\/m:mi>\n                              <m:mi>p<\/m:mi>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2021-0131_eq_0346.png\" \/>\n                        <jats:tex-math>{\\ell^{p}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-quasi-norm minimization. Compared to <jats:inline-formula id=\"j_cmam-2021-0131_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi mathvariant=\"normal\">\u2113<\/m:mi>\n                              <m:mn>1<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2021-0131_eq_0342.png\" \/>\n                        <jats:tex-math>{\\ell^{1}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-norm minimization, the choice of <jats:inline-formula id=\"j_cmam-2021-0131_ineq_9997\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mn>0<\/m:mn>\n                              <m:mo>&lt;<\/m:mo>\n                              <m:mi>p<\/m:mi>\n                              <m:mo>&lt;<\/m:mo>\n                              <m:mn>1<\/m:mn>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2021-0131_eq_0172.png\" \/>\n                        <jats:tex-math>{0&lt;p&lt;1}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> provides a natural framework to accommodate usual constraints which quadrature rules must fulfil.\nWe also extend an <jats:italic>a priori<\/jats:italic> error estimate available for the <jats:inline-formula id=\"j_cmam-2021-0131_ineq_9996\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi mathvariant=\"normal\">\u2113<\/m:mi>\n                              <m:mn>1<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2021-0131_eq_0342.png\" \/>\n                        <jats:tex-math>{\\ell^{1}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-norm formulation by considering the error resulting from data compression. Finally, we present numerical examples to investigate the numerical performance of our method and compare our results to both <jats:inline-formula id=\"j_cmam-2021-0131_ineq_9995\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi mathvariant=\"normal\">\u2113<\/m:mi>\n                              <m:mn>1<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2021-0131_eq_0342.png\" \/>\n                        <jats:tex-math>{\\ell^{1}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>-norm minimization and nonnegative least squares method. Matlab codes related to the numerical examples and the algorithms described are provided.<\/jats:p>","DOI":"10.1515\/cmam-2021-0131","type":"journal-article","created":{"date-parts":[[2022,2,14]],"date-time":"2022-02-14T12:21:23Z","timestamp":1644841283000},"page":"389-411","source":"Crossref","is-referenced-by-count":5,"title":["Sparse Data-Driven Quadrature Rules via \u2113<sup>\n                     <i>p<\/i>\n                  <\/sup>-Quasi-Norm Minimization"],"prefix":"10.1515","volume":"22","author":[{"given":"Mattia","family":"Manucci","sequence":"first","affiliation":[{"name":"Gran Sasso Science Institute , via Crispi 7 , L\u2019Aquila , Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jose Vicente","family":"Aguado","sequence":"additional","affiliation":[{"name":"\u00c9cole Centrale de Nantes , 1 Rue de la No\u00eb , Nantes , France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Domenico","family":"Borzacchiello","sequence":"additional","affiliation":[{"name":"\u00c9cole Centrale de Nantes , 1 Rue de la No\u00eb , Nantes , France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2022,2,15]]},"reference":[{"key":"2023033111281518601_j_cmam-2021-0131_ref_001","doi-asserted-by":"crossref","unstructured":"S. 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Farhat,\nAccelerated mesh sampling for the hyper reduction of nonlinear computational models,\nInternat. J. Numer. Methods Engrg. 109 (2017), no. 12, 1623\u20131654.","DOI":"10.1002\/nme.5332"},{"key":"2023033111281518601_j_cmam-2021-0131_ref_005","doi-asserted-by":"crossref","unstructured":"S.  Chaturantabut and D. C.  Sorensen,\nNonlinear model reduction via discrete empirical interpolation,\nSIAM J. Sci. Comput. 32 (2010), no. 5, 2737\u20132764.","DOI":"10.1137\/090766498"},{"key":"2023033111281518601_j_cmam-2021-0131_ref_006","doi-asserted-by":"crossref","unstructured":"G. B.  Dantzig, A.  Orden and P.  Wolfe,\nThe generalized simplex method for minimizing a linear form under linear inequality restraints,\nPacific J. Math. 5 (1955), 183\u2013195.","DOI":"10.2140\/pjm.1955.5.183"},{"key":"2023033111281518601_j_cmam-2021-0131_ref_007","doi-asserted-by":"crossref","unstructured":"M. E.  Davies and R.  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Lai,\nSparsest solutions of underdetermined linear systems via \n                  \n                     \n                        \n                           l\n                           q\n                        \n                     \n                     \n                     l_{q}\n                  \n               -minimization for \n                  \n                     \n                        \n                           0\n                           <\n                           q\n                           \u2264\n                           1\n                        \n                     \n                     \n                     0<q\\leq 1\n                  \n               ,\nAppl. Comput. Harmon. Anal. 26 (2009), no. 3, 395\u2013407.","DOI":"10.1016\/j.acha.2008.09.001"},{"key":"2023033111281518601_j_cmam-2021-0131_ref_011","doi-asserted-by":"crossref","unstructured":"S.  Grimberg, C.  Farhat, R.  Tezaur and C.  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Engrg. 344 (2019), 1104\u20131123.","DOI":"10.1016\/j.cma.2018.02.028"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0131\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0131\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T15:00:21Z","timestamp":1680274821000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2021-0131\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,15]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,11,5]]},"published-print":{"date-parts":[[2022,4,1]]}},"alternative-id":["10.1515\/cmam-2021-0131"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2021-0131","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,15]]}}}