{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T12:11:30Z","timestamp":1768738290601,"version":"3.49.0"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T00:00:00Z","timestamp":1596412800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T00:00:00Z","timestamp":1596412800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2021,2]]},"DOI":"10.1007\/s12190-020-01409-5","type":"journal-article","created":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T14:07:43Z","timestamp":1596463663000},"page":"651-667","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Modified Shepard\u2019s method by six-points local interpolant"],"prefix":"10.1007","volume":"65","author":[{"given":"Otheman","family":"Nouisser","sequence":"first","affiliation":[]},{"given":"Benaissa","family":"Zerroudi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,8,3]]},"reference":[{"key":"1409_CR1","volume-title":"Calculus, Volume I, One-Variable Calculus, with an Introduction to Linear Algebra","author":"TM Apostol","year":"2007","unstructured":"Apostol, T.M.: Calculus, Volume I, One-Variable Calculus, with an Introduction to Linear Algebra, vol. 1. Wiley, Hoboken (2007)"},{"issue":"2","key":"1409_CR2","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1016\/j.jat.2005.02.008","volume":"134","author":"C de Boor","year":"2005","unstructured":"de Boor, C.: An asymptotic expansion for the error in a linear map that reproduces polynomials of a certain order. J. Approx. Theory 134(2), 171\u2013174 (2005)","journal-title":"J. Approx. Theory"},{"issue":"257","key":"1409_CR3","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1090\/S0025-5718-06-01894-1","volume":"76","author":"R Caira","year":"2007","unstructured":"Caira, R., Dell\u2019Accio, F.: Shepard\u2013Bernoulli operators. Math. Comput. 76(257), 299\u2013321 (2007)","journal-title":"Math. Comput."},{"issue":"7","key":"1409_CR4","doi-asserted-by":"publisher","first-page":"1691","DOI":"10.1016\/j.cam.2011.10.001","volume":"236","author":"R Caira","year":"2012","unstructured":"Caira, R., Dell\u2019Accio, F., Di Tommaso, F.: On the bivariate Shepard\u2013Lidstone operators. J. Comput. Appl. Math. 236(7), 1691\u20131707 (2012)","journal-title":"J. Comput. Appl. Math."},{"issue":"1","key":"1409_CR5","doi-asserted-by":"crossref","first-page":"11","DOI":"10.33993\/jnaat321-730","volume":"32","author":"T C\u0103tina\u015f","year":"2003","unstructured":"C\u0103tina\u015f, T.: The combined Shepard\u2013Abel\u2013Goncharov univariate operator. Rev. Anal. Num\u00e9r. Th\u00e9or. Approx. 32(1), 11\u201320 (2003)","journal-title":"Rev. Anal. Num\u00e9r. Th\u00e9or. Approx."},{"issue":"4","key":"1409_CR6","first-page":"471","volume":"7","author":"G Coman","year":"2001","unstructured":"Coman, G.: Combined Shepard univariate operators. East J. Approx. 7(4), 471\u2013483 (2001)","journal-title":"East J. Approx."},{"issue":"11","key":"1409_CR7","doi-asserted-by":"publisher","first-page":"3641","DOI":"10.1016\/j.camwa.2012.10.004","volume":"64","author":"FA Costabile","year":"2012","unstructured":"Costabile, F.A., Dell\u2019Accio, F., Di Tommaso, F.: Enhancing the approximation order of local Shepard operators by Hermite polynomials. Comput. Math. Appl. 64(11), 3641\u20133655 (2012)","journal-title":"Comput. Math. Appl."},{"issue":"1","key":"1409_CR8","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1007\/s11075-012-9659-6","volume":"64","author":"FA Costabile","year":"2013","unstructured":"Costabile, F.A., DellAccio, F., Di Tommaso, F.: Complementary Lidstone interpolation on scattered data sets. Numer. Algorithms 64(1), 157\u2013180 (2013)","journal-title":"Numer. Algorithms"},{"issue":"2","key":"1409_CR9","first-page":"49","volume":"48","author":"I Cozac","year":"2003","unstructured":"Cozac, I.: Shepard method-from approximation to interpolation. Studia. Univ.Babe\u015f-Bolyai Math. 48(2), 49\u201352 (2003)","journal-title":"Studia. Univ.Babe\u015f-Bolyai Math."},{"key":"1409_CR10","first-page":"32","volume":"9","author":"F Dell\u2019 Accio","year":"2016","unstructured":"Dell\u2019 Accio, F., Di Tommaso, F.: Scattered data interpolation by Shepards like methods: classical results and recent advances. Dolomites Res. Notes Approx. 9, 32\u201344 (2016)","journal-title":"Dolomites Res. Notes Approx."},{"issue":"1","key":"1409_CR11","first-page":"1","volume":"12","author":"F Dell\u2019Accio","year":"2019","unstructured":"Dell\u2019Accio, F., Di Tommaso, F.: Rate of convergence of multinode Shepard operators. Dolomites Res. Notes Approx. 12(1), 1\u20136 (2019)","journal-title":"Dolomites Res. Notes Approx."},{"key":"1409_CR12","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.apnum.2019.09.005","volume":"150","author":"F Dell\u2019Accio","year":"2020","unstructured":"Dell\u2019Accio, F., Di Tommaso, F.: On the hexagonal Shepard method. Appl. Numer. Math. 150, 51\u201364 (2020)","journal-title":"Appl. Numer. Math."},{"key":"1409_CR13","first-page":"359","volume":"36","author":"F Dell\u2019Accio","year":"2016","unstructured":"Dell\u2019Accio, F., Di Tommaso, F., Hormann, K.: On the approximation order of triangular Shepard interpolation. IMA J. Numer. Anal. 36, 359\u2013379 (2016)","journal-title":"IMA J. Numer. Anal."},{"key":"1409_CR14","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1016\/j.apnum.2017.12.006","volume":"126","author":"F Dell\u2019Accio","year":"2018","unstructured":"Dell\u2019Accio, F., Di Tommaso, F., Nouisser, O., Zerroudi, B.: Increasing the approximation order of the triangular shepard method. Appl. Numer. Math. 126, 78\u201391 (2018)","journal-title":"Appl. Numer. Math."},{"key":"1409_CR15","doi-asserted-by":"crossref","unstructured":"Dell\u2019Accio, F., Di Tommaso, F., Nouisser, O., Zerroudi, B.: Fast and accurate scattered Hermite interpolation by triangular Shepard operators. J. Comput. Appl. Math. pp. 113\u2013092 (2020)","DOI":"10.1016\/j.cam.2020.113092"},{"issue":"9\u201310","key":"1409_CR16","doi-asserted-by":"publisher","first-page":"726","DOI":"10.1016\/j.ijmecsci.2009.08.004","volume":"51","author":"G Farrahi","year":"2009","unstructured":"Farrahi, G., Faghidian, S., Smith, D.: An inverse approach to determination of residual stresses induced by shot peening in round bars. Int. J. Mech. Sci. 51(9\u201310), 726\u2013731 (2009)","journal-title":"Int. J. Mech. Sci."},{"issue":"174","key":"1409_CR17","first-page":"577","volume":"46","author":"R Farwig","year":"1986","unstructured":"Farwig, R.: Rate of convergence of Shepard\u2019s global interpolation formula. Math. Comput. 46(174), 577\u2013590 (1986)","journal-title":"Math. Comput."},{"key":"1409_CR18","doi-asserted-by":"crossref","unstructured":"Franke, R.: A critical comparison of some methods for interpolation of scattered data. Technical Report NPS-53-79-003, Department of Mathematics, Naval Postgraduate School, Monterey, CA (1979)","DOI":"10.21236\/ADA081688"},{"issue":"157","key":"1409_CR19","first-page":"181","volume":"38","author":"R Franke","year":"1982","unstructured":"Franke, R.: Scattered data interpolation: Tests of some methods. Math. Comput. 38(157), 181\u2013200 (1982)","journal-title":"Math. Comput."},{"key":"1409_CR20","doi-asserted-by":"publisher","first-page":"1691","DOI":"10.1002\/nme.1620151110","volume":"15","author":"R Franke","year":"1980","unstructured":"Franke, R., Nielson, G.: Smooth interpolation of large sets of scatter data. Int. J. Numer. Methods Eng. 15, 1691\u20131704 (1980). https:\/\/doi.org\/10.1002\/nme.1620151110","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"1","key":"1409_CR21","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1016\/j.cam.2005.08.015","volume":"196","author":"A Guessab","year":"2006","unstructured":"Guessab, A., Nouisser, O., Schmeisser, G.: Multivariate approximation by a combination of modified Taylor polynomials. J. Comput. Appl. Math. 196(1), 162\u2013179 (2006)","journal-title":"J. Comput. Appl. Math."},{"issue":"17","key":"1409_CR22","doi-asserted-by":"publisher","first-page":"174116","DOI":"10.1063\/1.5124469","volume":"151","author":"K Karandashev","year":"2019","unstructured":"Karandashev, K., Van\u00ed\u010dek, J.: A combined on-the-fly\/interpolation procedure for evaluating energy values needed in molecular simulations. J. Chem. Phys. 151(17), 174116 (2019)","journal-title":"J. Chem. Phys."},{"issue":"9","key":"1409_CR23","doi-asserted-by":"publisher","first-page":"1599","DOI":"10.1002\/nme.1620200905","volume":"20","author":"T Liszka","year":"1984","unstructured":"Liszka, T.: An interpolation method for an irregular net of nodes. Int. J. Numer. Methods Eng. 20(9), 1599\u20131612 (1984)","journal-title":"Int. J. Numer. Methods Eng."},{"issue":"4","key":"1409_CR24","doi-asserted-by":"publisher","first-page":"318","DOI":"10.1093\/comjnl\/17.4.318","volume":"17","author":"DH McLain","year":"1974","unstructured":"McLain, D.H.: Drawing contours from arbitrary data points. Comput. J. 17(4), 318\u2013324 (1974)","journal-title":"Comput. J."},{"key":"1409_CR25","first-page":"2","volume":"14","author":"RJ Renka","year":"1988","unstructured":"Renka, R.J.: Multivariate interpolation of large sets of scattered data. ACM Trans. Math. Softw. 14, 2 (1988)","journal-title":"ACM Trans. Math. Softw."},{"issue":"1","key":"1409_CR26","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1145\/305658.305737","volume":"25","author":"RJ Renka","year":"1999","unstructured":"Renka, R.J.: Algorithm 790: CSHEP2D: Cubic method for bivariate interpolation of scattered data. ACM Trans. Math. Software 25(1), 70\u201373 (1999)","journal-title":"ACM Trans. Math. Software"},{"issue":"1","key":"1409_CR27","doi-asserted-by":"publisher","first-page":"78","DOI":"10.1145\/305658.305745","volume":"25","author":"RJ Renka","year":"1999","unstructured":"Renka, R.J., Brown, R.: Algorithm 792: accuracy tests of ACM algorithms for interpolation of scattered data in the plane. ACM Trans. Math. Softw. 25(1), 78\u201394 (1999)","journal-title":"ACM Trans. Math. Softw."},{"key":"1409_CR28","doi-asserted-by":"crossref","unstructured":"Shepard, D.: A two-dimensional interpolation function for irregularly-spaced data. In: Proceedings of the 1968 23rd ACM National Conference, ACM \u201968, pp. 517\u2013524. Association for Computing Machinery, New York (1968)","DOI":"10.1145\/800186.810616"},{"issue":"3","key":"1409_CR29","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1145\/1824801.1824812","volume":"37","author":"WI Thacker","year":"2010","unstructured":"Thacker, W.I., Zhang, J., Watson, L.T., Birch, J.B., Iyer, M.A., Berry, M.W.: Algorithm 905: SHEPPACK: Modified Shepard algorithm for interpolation of scattered multivariate data. ACM Trans. Math. Softw. 37(3), 20\u201334 (2010)","journal-title":"ACM Trans. Math. Softw."},{"issue":"2","key":"1409_CR30","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1016\/j.jat.2003.08.001","volume":"124","author":"H Xuli","year":"2003","unstructured":"Xuli, H.: Multi-node higher order expansions of a function. J. Approx. Theory 124(2), 242\u2013253 (2003)","journal-title":"J. Approx. Theory"}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01409-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-020-01409-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01409-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,11]],"date-time":"2024-08-11T07:26:26Z","timestamp":1723361186000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-020-01409-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,3]]},"references-count":30,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["1409"],"URL":"https:\/\/doi.org\/10.1007\/s12190-020-01409-5","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,3]]},"assertion":[{"value":"11 May 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 July 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 July 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 August 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}