{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T11:18:41Z","timestamp":1778671121183,"version":"3.51.4"},"reference-count":34,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2016,4,7]],"date-time":"2016-04-07T00:00:00Z","timestamp":1459987200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,4,7]],"date-time":"2016-04-07T00:00:00Z","timestamp":1459987200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000086","name":"Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","award":["1160633"],"award-info":[{"award-number":["1160633"]}],"id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[2016,10]]},"DOI":"10.1007\/s10444-016-9457-0","type":"journal-article","created":{"date-parts":[[2016,4,7]],"date-time":"2016-04-07T08:21:11Z","timestamp":1460017271000},"page":"1149-1186","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Cardinal interpolation with general multiquadrics"],"prefix":"10.1007","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0719-6045","authenticated-orcid":false,"given":"Keaton","family":"Hamm","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeff","family":"Ledford","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,4,7]]},"reference":[{"key":"9457_CR1","unstructured":"Abramowitz, M., Stegun, I.A. (eds.): Handbook of mathematical functions: with formulas, graphs, and mathematical tables. No 55 Courier Dover Publications (1972)"},{"issue":"4","key":"9457_CR2","doi-asserted-by":"publisher","first-page":"401","DOI":"10.1007\/BF01203461","volume":"8","author":"K Ball","year":"1992","unstructured":"Ball, K., Sivakumar, N., Ward, J.D.: On the sensitivity of radial basis interpolation to minimal data separation distance. Constr. Approx 8(4), 401\u2013426 (1992)","journal-title":"Constr. Approx"},{"issue":"12","key":"9457_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0898-1221(92)90166-F","volume":"24","author":"BJC Baxter","year":"1992","unstructured":"Baxter, B.J.C.: The asymptotic cardinal function of the multiquadratic $\\phi (r)=(r^{2}+ c^{2}){~}^{\\frac {1}{2}}$ as $c\\to \\infty $. Comput. Math. Appl. 24(12), 1\u20136 (1992)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"9457_CR4","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1006\/jath.1996.0091","volume":"87","author":"BJC Baxter","year":"1996","unstructured":"Baxter, B.J.C., Sivakumar, N.: On shifted cardinal interpolation by Gaussians and multiquadrics. J. Approx. Theory 87(1), 36\u201359 (1996)","journal-title":"J. Approx. Theory"},{"issue":"4","key":"9457_CR5","doi-asserted-by":"publisher","first-page":"434","DOI":"10.1016\/j.cam.2011.06.030","volume":"236","author":"RK Beatson","year":"2011","unstructured":"Beatson, R.K., Levesley, J., Mouat, C.T.: Better bases for radial basis function interpolation problems. J. Comput. Appl. Math 236(4), 434\u2013446 (2011)","journal-title":"J. Comput. Appl. Math"},{"key":"9457_CR6","unstructured":"Bennett, C., Sharpley, R.: Interpolation of operators new york (1988)"},{"key":"9457_CR7","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1007\/BF01890410","volume":"6.3","author":"M Buhmann","year":"1990","unstructured":"Buhmann, M.: Multivariate cardinal interpolation with radial-basis functions. Constr. Approx 6.3, 225\u2013255 (1990)","journal-title":"Constr. Approx"},{"issue":"1","key":"9457_CR8","first-page":"33","volume":"41","author":"M Buhmann","year":"1998","unstructured":"Buhmann, M.: Radial functions on compact support, Proc. Edinburgh. Math. Soc. (2) 41(1), 33\u201346 (1998)","journal-title":"Math. Soc. (2)"},{"key":"9457_CR9","doi-asserted-by":"crossref","unstructured":"Buhmann, M.: Radial basis functions: theory and implementations, Vol. 12 Cambridge University Press (2003)","DOI":"10.1017\/CBO9780511543241"},{"issue":"12","key":"9457_CR10","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/0898-1221(92)90168-H","volume":"24","author":"M Buhmann","year":"1992","unstructured":"Buhmann, M., Micchelli, C.A.: Multiquadric interpolation improved. Comput. Math. Appl 24(12), 21\u201325 (1992)","journal-title":"Comput. Math. Appl"},{"key":"9457_CR11","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/S0898-1221(01)00295-4","volume":"43","author":"T Driscoll","year":"2002","unstructured":"Driscoll, T., Fornberg, B.: Interpolation in the limit of increasingly flat radial basis functions. Comput. Math. Appl 43, 413\u2013422 (2002)","journal-title":"Comput. Math. Appl"},{"issue":"2","key":"9457_CR12","doi-asserted-by":"publisher","first-page":"A737","DOI":"10.1137\/110824784","volume":"34","author":"GE Fasshauer","year":"2012","unstructured":"Fasshauer, G.E., McCourt, M.J.: Stable evaluation of Gaussian radial basis function interpolants. SIAM J. Sci. Comput 34(2), A737\u2013A762 (2012)","journal-title":"SIAM J. Sci. Comput"},{"key":"9457_CR13","doi-asserted-by":"crossref","unstructured":"Fornberg, B., Flyer, N.: A primer on radial basis functions with applications to the geosciences, vol. 87 SIAM (2015)","DOI":"10.1137\/1.9781611974041"},{"issue":"2","key":"9457_CR14","doi-asserted-by":"publisher","first-page":"869","DOI":"10.1137\/09076756X","volume":"33","author":"B Fornberg","year":"2011","unstructured":"Fornberg, B., Larsson, E., Flyer, N.: Stable computations with Gaussian radial basis functions. SIAM J. Sci. Comput 33(2), 869\u2013892 (2011)","journal-title":"SIAM J. Sci. Comput"},{"issue":"1","key":"9457_CR15","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1016\/j.camwa.2005.01.010","volume":"49","author":"E Larsson","year":"2005","unstructured":"Larsson, E., Fornberg, B.: Theoretical and computational aspects of multivariate interpolation with increasingly flat radial basis functions. Comput. Math. Appl 49 (1), 103\u2013130 (2005)","journal-title":"Comput. Math. Appl"},{"issue":"5","key":"9457_CR16","doi-asserted-by":"publisher","first-page":"853","DOI":"10.1016\/j.camwa.2003.08.010","volume":"48","author":"B Fornberg","year":"2004","unstructured":"Fornberg, B., Wright, G.B.: Stable computation of multiquadric interpolants for all values of the shape parameter. Comput. Math. Appl 48(5), 853\u2013867 (2004)","journal-title":"Comput. Math. Appl"},{"issue":"5","key":"9457_CR17","doi-asserted-by":"publisher","first-page":"2538","DOI":"10.1137\/120876940","volume":"51","author":"E Fuselier","year":"2013","unstructured":"Fuselier, E., Hangelbroek, T., Narcowich, F.J., Ward, J.D., Wright, G.B.: Localized bases for kernel spaces on the unit sphere. SIAM J. Numer. Anal 51(5), 2538\u20132562 (2013)","journal-title":"SIAM J. Numer. Anal"},{"key":"9457_CR18","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1007\/s00041-011-9185-2","volume":"18","author":"T Hangelbroek","year":"2012","unstructured":"Hangelbroek, T., Madych, W., Narcowich, F., Ward, J.: Cardinal interpolation with Gaussian kernels. J. Fourier Anal. Appl 18, 67\u201386 (2012)","journal-title":"J. Fourier Anal. Appl"},{"key":"9457_CR19","unstructured":"Hangelbroek, T., Narcowich, F.J., Rieger, C., Ward, J.D.: An inverse theorem on bounded domains for meshless methods using localized bases. arXiv preprint arXiv:\n                    1406.1435\n                    \n                   (2014)"},{"issue":"4","key":"9457_CR20","doi-asserted-by":"publisher","first-page":"1732","DOI":"10.1137\/090769570","volume":"42","author":"T Hangelbroek","year":"2010","unstructured":"Hangelbroek, T., Narcowich, F.J., Ward, J.D.: Kernel approximation on manifolds I: Bounding the Lebesgue constant. SIAM J. Math. Anal 42(4), 1732\u20131760 (2010)","journal-title":"SIAM J. Math. Anal"},{"issue":"2","key":"9457_CR21","doi-asserted-by":"publisher","first-page":"662","DOI":"10.1137\/100795334","volume":"43","author":"T Hangelbroek","year":"2011","unstructured":"Hangelbroek, T., Narcowich, F.J., Sun, X., Ward, J.D.: Kernel approximation on manifolds II: the $L_{\\infty }$ norm of the L\n                           2 projector. SIAM J. Math. Anal 43(2), 662\u2013684 (2011)","journal-title":"SIAM J. Math. Anal"},{"key":"9457_CR22","doi-asserted-by":"crossref","unstructured":"Katznelson, Y.: An introduction to harmonic analysis, Third Edition, Dover (2004)","DOI":"10.1017\/CBO9781139165372"},{"issue":"2","key":"9457_CR23","doi-asserted-by":"publisher","first-page":"357","DOI":"10.1007\/s10444-014-9361-4","volume":"41","author":"J Ledford","year":"2015","unstructured":"Ledford, J.: On the convergence of regular families of cardinal interpolators. Adv. Comput. Math 41(2), 357\u2013371 (2015)","journal-title":"Adv. Comput. Math"},{"key":"9457_CR24","unstructured":"Ledford, J.: Convergence properties of spline-like cardinal interpolation operators acting on \u2113\n                           \n                    p\n                   data. (submitted) arXiv:\n                    1312.4062\n                    \n                   (2013)"},{"issue":"12","key":"9457_CR25","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/0898-1221(92)90175-H","volume":"24","author":"WR Madych","year":"1992","unstructured":"Madych, W.R.: Miscellaneous error bounds for multiquadric and related interpolators. Comput. Math. Appl 24(12), 121\u2013138 (1992)","journal-title":"Comput. Math. Appl"},{"key":"9457_CR26","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1512\/iumj.1975.24.24052","volume":"24","author":"MJ Marsden","year":"1975","unstructured":"Marsden, M.J., Richards, F.B., Riemenschneider, S.D.: Cardinal spline interpolation operators on \u2113\n                           \n                    p\n                   data. Indiana Univ. Math. J 24, 677-689 (1975). Erratum, ibid. 25 (1976), 919","journal-title":"Indiana Univ. Math. J"},{"key":"9457_CR27","unstructured":"Narcowich, F.J., Rowe, S.T., Ward, J.D.: A novel Galerkin method for solving PDEs on the sphere using highly localized kernel bases. arXiv preprint, arXiv:\n                    1404.5263\n                    \n                   (2014)"},{"key":"9457_CR28","first-page":"157","volume":"8","author":"SD Riemenschneider","year":"2000","unstructured":"Riemenschneider, S.D., Sivakumar, N.: Cardinal interpolation by Gaussian functions: a survey. J. Anal 8, 157\u2013178 (2000)","journal-title":"J. Anal"},{"issue":"4","key":"9457_CR29","first-page":"485","volume":"7","author":"SD Riemenschneider","year":"1999","unstructured":"Riemenschneider, S.D., Sivakumar, N.: On the Cardinal-interpolation Operator Associated with the One-dimensional Multiquadric,. East J. Approx 7(4), 485\u2013514 (1999)","journal-title":"East J. Approx"},{"key":"9457_CR30","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1007\/BF02788236","volume":"79","author":"SD Riemenschneider","year":"1999","unstructured":"Riemenschneider, S.D., Sivakumar, N.: On cardinal interpolation by Gaussian radial-basis functions: properties of fundamental functions and estimates for Lebesgue constants. J. Anal. Math 79, 33\u201361 (1999)","journal-title":"J. Anal. Math"},{"key":"9457_CR31","doi-asserted-by":"crossref","unstructured":"Schoenberg, I.J.: Cardinal spline interpolation, vol. 12. Society for Industrial and Applied Mathematics, Philadelphia (1973)","DOI":"10.1137\/1.9781611970555"},{"key":"9457_CR32","unstructured":"Watson, G.N.: A treatise on the theory of Bessel functions, Second Edition, Cambridge University Press (1944)"},{"key":"9457_CR33","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/BF02123482","volume":"4","author":"H Wendland","year":"1995","unstructured":"Wendland, H.: Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv. Comput. Math 4, 389\u2013396 (1995)","journal-title":"Adv. Comput. Math"},{"key":"9457_CR34","doi-asserted-by":"crossref","unstructured":"Wendland, H.: Scattered data approximation, Vol. 17 Cambridge University Press (2005)","DOI":"10.1017\/CBO9780511617539"}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9457-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10444-016-9457-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9457-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10444-016-9457-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,17]],"date-time":"2020-05-17T15:36:02Z","timestamp":1589729762000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10444-016-9457-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4,7]]},"references-count":34,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2016,10]]}},"alternative-id":["9457"],"URL":"https:\/\/doi.org\/10.1007\/s10444-016-9457-0","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4,7]]},"assertion":[{"value":"8 January 2015","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 February 2016","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2016","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}