{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T11:19:08Z","timestamp":1778671148594,"version":"3.51.4"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2011,12,3]],"date-time":"2011-12-03T00:00:00Z","timestamp":1322870400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2013,5]]},"DOI":"10.1007\/s10444-011-9263-7","type":"journal-article","created":{"date-parts":[[2011,12,3]],"date-time":"2011-12-03T14:31:06Z","timestamp":1322922666000},"page":"873-889","source":"Crossref","is-referenced-by-count":3,"title":["L p error estimates for approximation by Sobolev splines and Wendland functions on \u211d d"],"prefix":"10.1007","volume":"38","author":[{"given":"John Paul","family":"Ward","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2011,12,3]]},"reference":[{"key":"9263_CR1","doi-asserted-by":"crossref","first-page":"385","DOI":"10.5802\/aif.116","volume":"11","author":"N Aronszajn","year":"1961","unstructured":"Aronszajn, N., Smith, K.T.: Theory of Bessel potentials. I. Ann. Inst. Fourier 11, 385\u2013475 (1961)","journal-title":"I. Ann. Inst. Fourier"},{"issue":"2","key":"9263_CR2","doi-asserted-by":"crossref","first-page":"211","DOI":"10.5802\/aif.147","volume":"13","author":"N Aronszajn","year":"1963","unstructured":"Aronszajn, N., Szeptyki P.: On spaces of potentials connected with L p classes. Ann. Inst. Fourier 13(2), 211\u2013306 (1963)","journal-title":"Ann. Inst. Fourier"},{"key":"9263_CR3","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-322-96661-2","volume-title":"Spectral Synthesis","author":"JJ Benedetto","year":"1975","unstructured":"Benedetto, J.J.: Spectral Synthesis. Academic, London (1975)"},{"issue":"5","key":"9263_CR4","doi-asserted-by":"crossref","first-page":"928","DOI":"10.1109\/TSMCB.2005.847743","volume":"35","author":"O Buchtala","year":"2005","unstructured":"Buchtala, O., Klimek, M., Sick, B.: Evolutionary optimization of radial basis function classifiers for data mining applications. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 35(5), 928\u2013947 (2005)","journal-title":"IEEE Trans. Syst. Man Cybern., Part B, Cybern."},{"issue":"12","key":"9263_CR5","doi-asserted-by":"crossref","first-page":"6205","DOI":"10.1090\/S0002-9947-2010-05070-6","volume":"362","author":"R DeVore","year":"2010","unstructured":"DeVore, R., Ron, A.: Approximation using scattered shifts of a multivariate function. Trans. Am. Math. Soc. 362(12), 6205\u20136229 (2010)","journal-title":"Trans. Am. Math. Soc."},{"issue":"4","key":"9263_CR6","doi-asserted-by":"crossref","first-page":"689","DOI":"10.1109\/TCBB.2009.31","volume":"6","author":"LA Diago","year":"2009","unstructured":"Diago, L.A., Moreno, E.: Evaluation of geometric complementarity between molecular surfaces using compactly supported radial basis functions. IEEE\/ACM Trans. Comput. Biol. Bioinf. 6(4), 689\u2013694 (2009)","journal-title":"IEEE\/ACM Trans. Comput. Biol. Bioinf."},{"issue":"1","key":"9263_CR7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/imanum\/drh021","volume":"25","author":"AC Faul","year":"2005","unstructured":"Faul, A.C., Goodsell, G., Powell, M.J.D.: A Krylov subspace algorithm for multiquadric interpolation in many dimensions. IMA J. Numer. Anal. 25(1), 1\u201324 (2005)","journal-title":"IMA J. Numer. Anal."},{"issue":"12","key":"9263_CR8","doi-asserted-by":"crossref","first-page":"2421","DOI":"10.1016\/j.ins.2010.02.023","volume":"180","author":"D Fisch","year":"2010","unstructured":"Fisch, D., Hofmann, A., Sick, B.: On the versatility of radial basis function neural networks: a case study in the field of intrusion detection. Inf. Sci. 180(12), 2421\u20132439 (2010)","journal-title":"Inf. Sci."},{"key":"9263_CR9","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1016\/j.jcp.2007.05.009","volume":"226","author":"N Flyer","year":"2007","unstructured":"Flyer, N., Wright, G.: Transport schemes on a sphere using radial basis functions. J. Comp. Physiol. 226, 1059\u20131084 (2007)","journal-title":"J. Comp. Physiol."},{"issue":"2106","key":"9263_CR10","doi-asserted-by":"crossref","first-page":"1946","DOI":"10.1098\/rspa.2009.0033","volume":"465","author":"N Flyer","year":"2009","unstructured":"Flyer, N., Wright, G.: A radial basis function method for shallow water equations on a sphere. Proc. R. Soc. Lond., A Math. Phys. Eng. Sci. 465(2106), 1946\u20131976 (2009)","journal-title":"Proc. R. Soc. Lond., A Math. Phys. Eng. Sci."},{"key":"9263_CR11","volume-title":"Fourier Analysis and Its Applications","author":"GB Folland","year":"1992","unstructured":"Folland, G.B.: Fourier Analysis and Its Applications. Brooks\/Cole, Pacific Grove, CA (1992)"},{"key":"9263_CR12","series-title":"A Wiley-Interscience Publication","volume-title":"Real Analysis","author":"GB Folland","year":"1999","unstructured":"Folland, G.B.: Real Analysis. Modern Techniques and their Applications, 2nd edn. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York (1999)","edition":"2"},{"key":"9263_CR13","doi-asserted-by":"crossref","first-page":"1873","DOI":"10.1109\/TIP.2007.898969","volume":"16","author":"A Gelas","year":"2007","unstructured":"Gelas, A., Bernard, O., Friboulet, D., Prost, R.: Compactly supported radial basis functions based collocation method for level-set evolution in image segmentation. IEEE Trans. Image Process. 16, 1873\u20131887 (2007)","journal-title":"IEEE Trans. Image Process."},{"key":"9263_CR14","unstructured":"Hangelbroek, T.: Approximation by scattered translates of the fundamental solution of the biharmonic equation on bounded domains. PhD Thesis. The University of Wisconsin, Madison (2007)"},{"issue":"1","key":"9263_CR15","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s00365-007-0679-8","volume":"28","author":"T Hangelbroek","year":"2008","unstructured":"Hangelbroek, T.: Error estimates for thin plate spline approximation in the disk. Constr. Approx. 28(1), 27\u201359 (2008)","journal-title":"Constr. Approx."},{"issue":"3","key":"9263_CR16","doi-asserted-by":"crossref","first-page":"1171","DOI":"10.1214\/009053607000000677","volume":"36","author":"T Hofmann","year":"2008","unstructured":"Hofmann, T., Sch\u00f6lkopf, B., Smola, A.J.: Kernel methods in machine learning. Ann. Stat. 36(3), 1171\u20131220 (2008)","journal-title":"Ann. Stat."},{"key":"9263_CR17","first-page":"263","volume":"23","author":"OE Livne","year":"2006","unstructured":"Livne, O.E., Wright, G.B.: Fast multilevel evaluation of smooth radial basis function expansions. Electron. Trans. Numer. Anal. 23, 263\u2013287 (2006)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"9263_CR18","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1090\/S0025-5718-09-02322-9","volume":"79","author":"HN Mhaskar","year":"2010","unstructured":"Mhaskar, H.N., Narcowich, F.J., Prestin, J., Ward, J.D.: L p Bernstein estimates and approximation by spherical basis functions. Math. Comput. 79, 1647\u20131679 (2010)","journal-title":"Math. Comput."},{"key":"9263_CR19","volume-title":"Singular Integrals and Differentiability Properties of Functions","author":"EM Stein","year":"1970","unstructured":"Stein, E.M.: Singular Integrals and Differentiability Properties of Functions. Princeton University Press, Princeton, NJ (1970)"},{"key":"9263_CR20","volume-title":"Scattered Data Approximation","author":"H Wendland","year":"2005","unstructured":"Wendland, H.: Scattered Data Approximation. Cambridge University Press, Cambridge, UK (2005)"},{"issue":"25\u201328","key":"9263_CR21","doi-asserted-by":"crossref","first-page":"1793","DOI":"10.1016\/j.cma.2010.02.008","volume":"199","author":"R Yokota","year":"2010","unstructured":"Yokota, R., Barba, L.A., Knepley, M.G.: PetRBF-a parallel $\\mathcal{O}(N)$ algorithm for radial basis function interpolation with Gaussians. Comput. Methods Appl. Mech. Eng. 199(25\u201328), 1793\u20131804 (2010)","journal-title":"Comput. Methods Appl. Mech. Eng."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9263-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-011-9263-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-011-9263-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T17:08:16Z","timestamp":1559149696000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-011-9263-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12,3]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2013,5]]}},"alternative-id":["9263"],"URL":"https:\/\/doi.org\/10.1007\/s10444-011-9263-7","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,12,3]]}}}