{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T06:57:19Z","timestamp":1781333839252,"version":"3.54.1"},"reference-count":35,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100024370","name":"Ministero dell'Istruzione dell'Universita e della Ricerca","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100024370","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics Letters"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.aml.2026.110005","type":"journal-article","created":{"date-parts":[[2026,5,18]],"date-time":"2026-05-18T06:03:35Z","timestamp":1779084215000},"page":"110005","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Refined rates of convergence for target-data dependent greedy generalized interpolation with Sobolev kernels"],"prefix":"10.1016","volume":"181","author":[{"given":"Bernard","family":"Haasdonk","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6959-1070","authenticated-orcid":false,"given":"Gabriele","family":"Santin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tizian","family":"Wenzel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Daniel","family":"Winkle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.aml.2026.110005_b1","first-page":"Online","article-title":"Theory of reproducing kernels and applications","author":"Saitoh","year":"2016"},{"issue":"3","key":"10.1016\/j.aml.2026.110005_b2","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1214\/24-STS923","article-title":"The mat\u00e9rn model: A journey through statistics, numerical analysis and machine learning","volume":"39","author":"Porcu","year":"2024","journal-title":"Statist. Sci."},{"issue":"1","key":"10.1016\/j.aml.2026.110005_b3","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/BF02123482","article-title":"Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree","volume":"4","author":"Wendland","year":"1995","journal-title":"Adv. Comput. Math."},{"issue":"1","key":"10.1016\/j.aml.2026.110005_b4","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s10444-008-9089-0","article-title":"Sampling inequalities for infinitely smooth functions, with applications to interpolation and machine learning","volume":"32","author":"Rieger","year":"2008","journal-title":"Adv. Comput. Math."},{"key":"10.1016\/j.aml.2026.110005_b5","article-title":"Scattered data approximation","volume":"vol. 17","author":"Wendland","year":"2005"},{"key":"10.1016\/j.aml.2026.110005_b6","series-title":"Surface Fitting and Multiresolution Methods a. Le M\u00c9haut\u00c9, C. Rabut and L.L. Schumaker (Eds.), Vanderbilt","first-page":"131","article-title":"Solving partial differential equations by collocation with radial basis functions","author":"Fasshauer","year":"1997"},{"issue":"3","key":"10.1016\/j.aml.2026.110005_b7","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/s10444-004-1829-1","article-title":"Near-optimal data-independent point locations for radial basis function interpolation","volume":"23","author":"De Marchi","year":"2005","journal-title":"Adv. Comput. Math."},{"issue":"3","key":"10.1016\/j.aml.2026.110005_b8","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1023\/A:1019105612985","article-title":"Adaptive greedy techniques for approximate solution of large RBF systems","volume":"24","author":"Schaback","year":"2000","journal-title":"Numer. Algorithms"},{"key":"10.1016\/j.aml.2026.110005_b9","series-title":"Komplexit\u00e4t und Stabilit\u00e4t von kernbasierten Rekonstruktionsmethoden (Complexity and Stability of Kernel-based Reconstructions)","author":"M\u00fcller","year":"2009"},{"issue":"1","key":"10.1016\/j.aml.2026.110005_b10","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s00365-022-09592-3","article-title":"Analysis of target data-dependent greedy kernel algorithms: Convergence rates for f-, f\u22c5P- and f\/P-greedy","volume":"57","author":"Wenzel","year":"2023","journal-title":"Constr. Approx."},{"key":"10.1016\/j.aml.2026.110005_b11","series-title":"A greedy method for solving classes of PDE problems","author":"Schaback","year":"2019"},{"issue":"1","key":"10.1016\/j.aml.2026.110005_b12","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/s10543-025-01053-0","article-title":"Adaptive meshfree approximation for linear elliptic partial differential equations with PDE-greedy kernel methods","volume":"65","author":"Wenzel","year":"2025","journal-title":"BIT Numer. Math."},{"issue":"1","key":"10.1016\/j.aml.2026.110005_b13","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1007\/s10543-024-01048-3","article-title":"On the convergence of generalized kernel-based interpolation by greedy data selection algorithms","volume":"65","author":"Albrecht","year":"2024","journal-title":"BIT Numer. Math."},{"key":"10.1016\/j.aml.2026.110005_b14","first-page":"68","article-title":"Convergence rate of the data-independent P-greedy algorithm in kernel-based approximation","volume":"10","author":"Santin","year":"2017","journal-title":"Dolomites Res. Notes Approx."},{"key":"10.1016\/j.aml.2026.110005_b15","doi-asserted-by":"crossref","DOI":"10.1016\/j.jat.2020.105508","article-title":"A novel class of stabilized greedy kernel approximation algorithms: Convergence, stability and uniform point distribution","volume":"262","author":"Wenzel","year":"2021","journal-title":"J. Approx. Theory"},{"issue":"5","key":"10.1016\/j.aml.2026.110005_b16","doi-asserted-by":"crossref","first-page":"2249","DOI":"10.1137\/23M1587956","article-title":"On the optimality of target-data-dependent kernel greedy interpolation in Sobolev reproducing kernel Hilbert spaces","volume":"62","author":"Santin","year":"2024","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.aml.2026.110005_b17","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9982-5","article-title":"Introduction to smooth manifolds","author":"Lee","year":"2012"},{"key":"10.1016\/j.aml.2026.110005_b18","doi-asserted-by":"crossref","DOI":"10.1090\/gsm\/019","article-title":"Partial differential equations","author":"Evans","year":"2010"},{"issue":"1","key":"10.1016\/j.aml.2026.110005_b19","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1137\/050633366","article-title":"Convergence of unsymmetric kernel-based meshless collocation methods","volume":"45","author":"Schaback","year":"2007","journal-title":"SIAM J. Numer. Anal."},{"key":"10.1016\/j.aml.2026.110005_b20","doi-asserted-by":"crossref","DOI":"10.1016\/j.physd.2025.134662","article-title":"Kernel methods for the approximation of the eigenfunctions of the koopman operator","volume":"476","author":"Lee","year":"2025","journal-title":"Phys. D: Nonlinear Phenom."},{"key":"10.1016\/j.aml.2026.110005_b21","series-title":"Toward efficient kernel-based solvers for nonlinear PDEs","author":"Xu","year":"2025"},{"key":"10.1016\/j.aml.2026.110005_b22","series-title":"Kernel-based greedy approximation of parametric elliptic boundary value problems","author":"Haasdonk","year":"2025"},{"issue":"4","key":"10.1016\/j.aml.2026.110005_b23","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1016\/j.cam.2011.05.021","article-title":"Bases for kernel-based spaces","volume":"236","author":"Pazouki","year":"2011","journal-title":"J. Comput. Appl. Math."},{"issue":"3","key":"10.1016\/j.aml.2026.110005_b24","doi-asserted-by":"crossref","first-page":"290","DOI":"10.1016\/0022-1236(81)90076-8","article-title":"Entropy numbers, s-numbers, and eigenvalue problems","volume":"41","author":"Carl","year":"1981","journal-title":"J. Funct. Anal."},{"key":"10.1016\/j.aml.2026.110005_b25","first-page":"xvi+601","article-title":"Support vector machines","author":"Steinwart","year":"2008"},{"issue":"05","key":"10.1016\/j.aml.2026.110005_b26","doi-asserted-by":"crossref","first-page":"779","DOI":"10.1142\/S0218202524500143","article-title":"Entropy-based convergence rates of greedy algorithms","volume":"34","author":"Li","year":"2024","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"5","key":"10.1016\/j.aml.2026.110005_b27","doi-asserted-by":"crossref","first-page":"555","DOI":"10.1016\/j.jco.2014.03.005","article-title":"Entropy numbers of convex hulls in Banach spaces and applications","volume":"30","author":"Carl","year":"2014","journal-title":"J. Complexity"},{"issue":"4","key":"10.1016\/j.aml.2026.110005_b28","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1112\/S0024609304003121","article-title":"Entropy of absolute convex hulls in Hilbert Spaces","volume":"36","author":"Gao","year":"2004","journal-title":"Bull. Lond. Math. Soc."},{"key":"10.1016\/j.aml.2026.110005_b29","first-page":"xii+649","article-title":"Constructive approximation: Advanced problems","volume":"vol. 304","author":"Lorentz","year":"1996"},{"key":"10.1016\/j.aml.2026.110005_b30","article-title":"Sharp bounds on the approximation rates, metric entropy, and n-widths of shallow neural networks","author":"Siegel","year":"2022","journal-title":"Found. Comput. Math."},{"key":"10.1016\/j.aml.2026.110005_b31","series-title":"Partial Differential Equations I: Basic Theory","volume":"vol. 115","author":"Taylor","year":"1996"},{"key":"10.1016\/j.aml.2026.110005_b32","series-title":"Symplecticity-preserving prediction of Hamiltonian dynamics by generalized kernel interpolation","author":"Herkert","year":"2026"},{"issue":"2","key":"10.1016\/j.aml.2026.110005_b33","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s00365-005-0624-7","article-title":"Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions","volume":"24","author":"Narcowich","year":"2006","journal-title":"Constr. Approx."},{"key":"10.1016\/j.aml.2026.110005_b34","series-title":"Convergence analysis of a greedy algorithm for conditioning Gaussian random variables","author":"Winkle","year":"2025"},{"issue":"3","key":"10.1016\/j.aml.2026.110005_b35","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1007\/s00365-013-9186-2","article-title":"Greedy algorithms for reduced bases in Banach spaces","volume":"37","author":"DeVore","year":"2013","journal-title":"Constr. Approx."}],"container-title":["Applied Mathematics Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965926001369?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0893965926001369?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T06:44:42Z","timestamp":1781333082000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0893965926001369"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":35,"alternative-id":["S0893965926001369"],"URL":"https:\/\/doi.org\/10.1016\/j.aml.2026.110005","relation":{},"ISSN":["0893-9659"],"issn-type":[{"value":"0893-9659","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Refined rates of convergence for target-data dependent greedy generalized interpolation with Sobolev kernels","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics Letters","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.aml.2026.110005","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"110005"}}