{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T06:30:13Z","timestamp":1777617013936,"version":"3.51.4"},"reference-count":70,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"2","license":[{"start":{"date-parts":[[2012,2,1]],"date-time":"2012-02-01T00:00:00Z","timestamp":1328054400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/ieeexplore.ieee.org\/Xplorehelp\/downloads\/license-information\/IEEE.html"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Inform. Theory"],"published-print":{"date-parts":[[2012,2]]},"DOI":"10.1109\/tit.2011.2169531","type":"journal-article","created":{"date-parts":[[2012,2,7]],"date-time":"2012-02-07T21:19:58Z","timestamp":1328649598000},"page":"1203-1214","source":"Crossref","is-referenced-by-count":45,"title":["Dependence of Computational Models on Input Dimension: Tractability of Approximation and Optimization Tasks"],"prefix":"10.1109","volume":"58","author":[{"given":"Paul C.","family":"Kainen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V\u011bra","family":"Kurkova","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcello","family":"Sanguineti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"ref70","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.04.007"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2006.12.009"},{"key":"ref38","first-page":"401","article-title":"Some enhancement to approximation of one-variable functions by orthonormal basis","volume":"19","author":"beliczyinski","year":"2009","journal-title":"Neural Netw World"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2003.11.004"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.1994.1004"},{"key":"ref31","author":"traub","year":"1999","journal-title":"Complexity and Information"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.2001.0601"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-04921-7_2"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1006\/jath.1998.3304"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-69894-1"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2008.08.001"},{"key":"ref60","author":"ekeland","year":"1983","journal-title":"Convexity and Optimization Infinite Dimensions I"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-009-9620-6"},{"key":"ref61","author":"gelfand","year":"1963","journal-title":"Calculus of Variations"},{"key":"ref63","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-010-9680-7"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(98)00039-2"},{"key":"ref64","first-page":"811","article-title":"Condition numbers and Ritz type methods in unconstrained optimization","volume":"36","author":"zolezzi","year":"2007","journal-title":"Contr Cybern"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2008.20.1.252"},{"key":"ref65","author":"daniel","year":"1971","journal-title":"The Approximate Minimization of Functionals"},{"key":"ref66","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0043612"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1109\/18.971754"},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-01-00923-5"},{"key":"ref68","first-page":"537","article-title":"The mathematics of learning: Dealing with data","volume":"50","author":"poggio","year":"2003","journal-title":"Notices Amer Math Soc"},{"key":"ref69","author":"vapnik","year":"1998","journal-title":"Statistical Learning Theory"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0005-1098(95)00119-1"},{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1007\/s10957-008-9471-6"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1145\/168304.168357"},{"key":"ref22","first-page":"97","author":"girosi","year":"1993","journal-title":"Artif Neural Netw Speech Vis"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1007\/BF02678464"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348546"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1506"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1145\/1008328.1008329"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1006\/jath.1996.0031"},{"key":"ref50","first-page":"271","author":"kon","year":"2006","journal-title":"Wavelets Splines"},{"key":"ref51","first-page":"67","article-title":"Extending Girosi's approximation estimates for functions in Sobolev spaces via statistical learning theory","volume":"3","author":"kon","year":"2005","journal-title":"J Anal Applicat"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623497315768"},{"key":"ref58","author":"anderson","year":"1987","journal-title":"Linear Programming in Infinite-Dimensional Spaces"},{"key":"ref57","volume":"ii","author":"courant","year":"1988","journal-title":"Differential and Integral Calculus"},{"key":"ref56","author":"adams","year":"2003","journal-title":"Sobolev Spaces"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(91)90075-G"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1002\/mana.200710029"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(97)00028-2"},{"key":"ref52","first-page":"153","article-title":"Approximation error bounds via Rademacher complexity","volume":"2","author":"gnecco","year":"2008","journal-title":"Appl Math Sci"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2011.05.014"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2010.10.002"},{"key":"ref40","author":"kolmogorov","year":"1970","journal-title":"Introductory Real Analysis"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2005.860474"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1109\/18.945285"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-41583-2"},{"key":"ref15","author":"haykin","year":"1998","journal-title":"Neural Networks A Comprehensive Foundation"},{"key":"ref16","author":"bellman","year":"1957","journal-title":"Dynamic Programming"},{"key":"ref17","first-page":"69","article-title":"Neural net approximation","author":"barron","year":"1992","journal-title":"Proc 7th Yale Workshop on Adaptive and Learning Systems"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1109\/18.256500"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1109\/18.256506"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1080.0317"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2004.11.002"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1109\/72.572089"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.2006383"},{"key":"ref8","author":"zoppoli","year":"0","journal-title":"Neural Approximations for Optimal Control and Decision"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.11.1.15"},{"key":"ref49","first-page":"295","article-title":"Approximation error bounds that use VC- bounds","author":"girosi","year":"1995","journal-title":"Proc Intl Conf on Artificial Neural Networks"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1013662124879"},{"key":"ref46","author":"hamming","year":"1986","journal-title":"Coding and Information Theory"},{"key":"ref45","article-title":"Remarques sur un résultat non publié de B. Maurey","volume":"i","author":"pisier","year":"0","journal-title":"Sm Anal Fonctionnelle 198081"},{"key":"ref48","author":"stein","year":"1970","journal-title":"Singular Integrals and Differentiability Properties of Functions"},{"key":"ref47","author":"martnez","year":"2001","journal-title":"The Theory of Fractional Powers of Operators"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1137\/S1052623403426507"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1996-5_16"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2009.04-08-745"},{"key":"ref43","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1007\/978-3-642-04274-4_73","volume":"5768","author":"krkov","year":"2009","journal-title":"Lecture Notes in Computer Science"}],"container-title":["IEEE Transactions on Information Theory"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx5\/18\/6145469\/06145504.pdf?arnumber=6145504","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,10]],"date-time":"2021-10-10T23:47:19Z","timestamp":1633909639000},"score":1,"resource":{"primary":{"URL":"http:\/\/ieeexplore.ieee.org\/document\/6145504\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,2]]},"references-count":70,"journal-issue":{"issue":"2"},"URL":"https:\/\/doi.org\/10.1109\/tit.2011.2169531","relation":{},"ISSN":["0018-9448","1557-9654"],"issn-type":[{"value":"0018-9448","type":"print"},{"value":"1557-9654","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,2]]}}}