{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T16:29:58Z","timestamp":1778948998469,"version":"3.51.4"},"reference-count":16,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11271041"],"award-info":[{"award-number":["11271041"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10931004"],"award-info":[{"award-number":["10931004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["2010DFR00700"],"award-info":[{"award-number":["2010DFR00700"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Key Foundation of China","doi-asserted-by":"crossref","award":["11271041"],"award-info":[{"award-number":["11271041"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Key Foundation of China","doi-asserted-by":"crossref","award":["10931004"],"award-info":[{"award-number":["10931004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Key Foundation of China","doi-asserted-by":"crossref","award":["2010DFR00700"],"award-info":[{"award-number":["2010DFR00700"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"International Science and Technology Cooperation Project of China","award":["11271041"],"award-info":[{"award-number":["11271041"]}]},{"name":"International Science and Technology Cooperation Project of China","award":["10931004"],"award-info":[{"award-number":["10931004"]}]},{"name":"International Science and Technology Cooperation Project of China","award":["2010DFR00700"],"award-info":[{"award-number":["2010DFR00700"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mi>x<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>y<\/mml:mi><\/mml:math>) is divided into two types: interior point and exterior point. The value of Hermite interpolation polynomial on a triangle will be used as the approximate value if point (<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>x<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>y<\/mml:mi><\/mml:math>) is an interior point, while the value of a Hermite interpolation function with the form of weighted combination will be used if it is an exterior point. Hermite interpolation needs the first-order derivatives of the interpolated function which is not directly given in scatted data, so this paper also gives the approximate derivative at every scatted point using local radial basis function interpolation. And numerical tests indicate that the proposed piecewise bivariate Hermite interpolations are economic and have good approximation capacity.<\/jats:p>","DOI":"10.1155\/2013\/239703","type":"journal-article","created":{"date-parts":[[2013,4,8]],"date-time":"2013-04-08T21:01:14Z","timestamp":1365454874000},"page":"1-10","source":"Crossref","is-referenced-by-count":6,"title":["Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data"],"prefix":"10.1155","volume":"2013","author":[{"given":"Renzhong","family":"Feng","sequence":"first","affiliation":[{"name":"School of Mathematics and Systematic Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China"},{"name":"Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Systematic Science, Beijing University of Aeronautics and Astronautics, Beijing 100191, China"},{"name":"Key Laboratory of Mathematics, Informatics and Behavioral Semantics, Ministry of Education, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"15","volume":"2012","year":"2012","journal-title":"Journal of Applied Mathematics"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.08.090"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2009.2028871"},{"issue":"1","key":"2","first-page":"67","volume":"23","year":"2005","journal-title":"Journal of Computational Mathematics"},{"issue":"4","key":"1","first-page":"830","volume":"14","year":"2003","journal-title":"Journal of Software"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1109\/2945.620490"},{"issue":"6","key":"4","first-page":"20","volume":"49","year":"2010","journal-title":"Acta Scientiarum Naturalium Universitatis Sunyatseni"},{"issue":"2","key":"5","first-page":"1","volume":"19","year":"2002","journal-title":"Chinese Journal of Engineering Mathematics"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(01)00485-X"},{"issue":"1","key":"7","first-page":"66","volume":"17","year":"2007","journal-title":"Computer Aided Drafting, Design and Manufacturing"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(98)00043-0"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/BF03177515"},{"issue":"2","key":"10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/BF02836101","volume":"8","year":"1992","journal-title":"Approximation Theory and Its Applications"},{"key":"11","first-page":"361","volume":"4","year":"2007","journal-title":"Journal of Information Computational Science"},{"key":"13","first-page":"793","volume":"7","year":"1934","journal-title":"Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1620151110"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/239703.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/239703.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/239703.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T14:28:16Z","timestamp":1715178496000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/239703\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":16,"alternative-id":["239703","239703"],"URL":"https:\/\/doi.org\/10.1155\/2013\/239703","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}