{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,10]],"date-time":"2024-06-10T12:35:49Z","timestamp":1718022949955},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1994,1,1]],"date-time":"1994-01-01T00:00:00Z","timestamp":757382400000},"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":[[1994,1]]},"DOI":"10.1007\/bf02519037","type":"journal-article","created":{"date-parts":[[2006,11,7]],"date-time":"2006-11-07T18:42:12Z","timestamp":1162924932000},"page":"81-99","source":"Crossref","is-referenced-by-count":27,"title":["Least squares surface approximation to scattered data using multiquadratic functions"],"prefix":"10.1007","volume":"2","author":[{"given":"Richard","family":"Franke","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hans","family":"Hagen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gregory M.","family":"Nielson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"BF02519037_CR1","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0898-1221(92)90168-H","volume":"24","author":"M.D. Buhmann","year":"1992","unstructured":"M.D. Buhmann and C.A. Micchelli, Multiquadric interpolation improved, Comp. Math. Appl. 24(1992)21\u201326.","journal-title":"Comp. Math. Appl."},{"key":"BF02519037_CR2","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1016\/0898-1221(91)90123-L","volume":"21","author":"R.E. Carlson","year":"1991","unstructured":"R.E. Carlson and T.A. Foley, The parameterR 2 in multiquadric interpolation, Comp. Math. Appl. 21(1991)29\u201342.","journal-title":"Comp. Math. Appl."},{"key":"BF02519037_CR3","doi-asserted-by":"crossref","unstructured":"J. Duchon, Splines minimizing rotation-invariant seminorms in Sobolev spaces, in:Multivariate Approximation Theory, ed. W. Schempp and K. Zeller (Birkh\u00e4user, 1979) pp. 85\u2013100.","DOI":"10.1007\/BFb0086566"},{"key":"BF02519037_CR4","doi-asserted-by":"crossref","unstructured":"R. Franke and G.M. Nielson, Scattered data interpolation and applications: A tutorial and survey, in:Geometric Modelling: Methods and Their Applications, ed. H. Hagen and D. Roller (Springer, 1991) pp. 131\u2013160.","DOI":"10.1007\/978-3-642-76404-2_6"},{"key":"BF02519037_CR5","first-page":"181","volume":"38","author":"R. Franke","year":"1982","unstructured":"R. Franke, Scattered data interpolation: Tests of some methods, Math. Comp. 38(1982)181\u2013200.","journal-title":"Math. Comp."},{"key":"BF02519037_CR6","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/0167-8396(85)90011-1","volume":"2","author":"R. Franke","year":"1985","unstructured":"R. Franke, Thin plate splines with tension, Comp. Aided Geom. Design 2(1985)87\u201395.","journal-title":"Comp. Aided Geom. Design"},{"key":"BF02519037_CR7","doi-asserted-by":"crossref","unstructured":"R. Franke, Approximation of scattered data for meteorological applications, in:Multivariate Approximation and Interpolation, ed. W. Haussman and K. Jetter (Birkh\u00e4user, 1990) pp. 107\u2013120.","DOI":"10.1007\/978-3-0348-5685-0_7"},{"key":"BF02519037_CR8","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0898-1221(92)90172-E","volume":"24","author":"F. Girosi","year":"1992","unstructured":"F. Girosi, On some extensions of radial basis functions and their applications in artificial intelligence, Comp. Math. Appl. 24(1992)61\u201380.","journal-title":"Comp. Math. Appl."},{"key":"BF02519037_CR9","doi-asserted-by":"crossref","first-page":"189","DOI":"10.2514\/3.44330","volume":"9","author":"R.L. Harder","year":"1972","unstructured":"R.L. Harder and R.N. Desmarais, Interpolation using surface splines, J. Aircraft 9(1972)189\u2013191.","journal-title":"J. Aircraft"},{"key":"BF02519037_CR10","doi-asserted-by":"crossref","first-page":"1905","DOI":"10.1029\/JB076i008p01905","volume":"76","author":"R.L. Hardy","year":"1971","unstructured":"R.L. Hardy, Multiquadric equations of topography and other irregular surfaces, J. Geophys. Res. 76(1971)1905\u20131915.","journal-title":"J. Geophys. Res."},{"key":"BF02519037_CR11","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1016\/0898-1221(90)90272-L","volume":"19","author":"R.L. Hardy","year":"1990","unstructured":"R.L. Hardy, Theory and applications of the multiquadric-biharmonic method. Comp. Math. Appl. 19(1990)163\u2013208.","journal-title":"Comp. Math. Appl."},{"key":"BF02519037_CR12","doi-asserted-by":"crossref","unstructured":"H. Hagen and G. Schulze, Variational principles in curve and surface design, in:Geometric Modelling: Methods and Applications, ed. Hagen and Roller (Springer, 1991) pp. 161\u2013184.","DOI":"10.1007\/978-3-642-76404-2_7"},{"key":"BF02519037_CR13","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/0898-1221(92)90174-G","volume":"24","author":"E.J. Kansa","year":"1992","unstructured":"E.J. Kansa and R.E. Carlson, Improved accuracy of multiquadric interpolation using variable shape parameters, Comp. Math. Appl. 24(1992)99\u2013120.","journal-title":"Comp. Math. Appl."},{"key":"BF02519037_CR14","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1007\/BF01893414","volume":"2","author":"C.A. Micchelli","year":"1986","unstructured":"C.A. Micchelli, Interpolation of scattered data: Distance matrices and conditionally positive definite functions, Const. Approx. 2(1986)11\u201322.","journal-title":"Const. Approx."},{"key":"BF02519037_CR15","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1137\/0913026","volume":"13","author":"J. McMahon","year":"1992","unstructured":"J. McMahon and R. Franke, Knot selection for least squares thin plate splines, SIAM J. Sci. Stat. Comput. 13(1992)484\u2013498.","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"BF02519037_CR16","doi-asserted-by":"crossref","unstructured":"G.M. Nielson and T. Foley, A survey of applications of an affine invariant norm, in:Mathematical Methods in CAGD, ed. T. Lyche and L. Schumaker (Academic Press, 1989) pp. 445\u2013467.","DOI":"10.1016\/B978-0-12-460515-2.50036-6"},{"key":"BF02519037_CR17","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1002\/nme.1620150214","volume":"15","author":"G.M. Nielson","year":"1978","unstructured":"G.M. Nielson, A first-order blending method for triangles based upon cubic interpolation, Int. J. Numer. Meth. Eng. 15(1978)308\u2013318.","journal-title":"Int. J. Numer. Meth. Eng."},{"key":"BF02519037_CR18","doi-asserted-by":"crossref","unstructured":"M.J.D. Powell, Wavelets, subdivision algorithms and radial basis functions, in:Advances in Numerical Analysis, Vol. 2, ed. W.A. Light (Clarendon Press, 1992) pp. 105\u2013210.","DOI":"10.1093\/oso\/9780198534396.003.0003"},{"key":"BF02519037_CR19","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0898-1221(92)90178-K","volume":"24","author":"K. Salkauskas","year":"1992","unstructured":"K. Salkauskas, Moving least squares interpolation with thin-plate splines and radial basis functions, Comp. Math. Appl. 24(1992)177\u2013186.","journal-title":"Comp. Math. Appl."},{"key":"BF02519037_CR20","unstructured":"A.E. Tarwater, A parameter study of Hardy\u2019s multiquadric method for scattered data interpolation, Report TR UCRL-53670, Lawrence Livermore National Laboratory (1985)."},{"key":"BF02519037_CR21","unstructured":"D.J. Woods, Report 85-5, Dept. Math. Sciences, Rice University (1985)."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02519037.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02519037\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02519037","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T05:22:25Z","timestamp":1707369745000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02519037"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1994,1]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1994,1]]}},"alternative-id":["BF02519037"],"URL":"https:\/\/doi.org\/10.1007\/bf02519037","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[1994,1]]}}}