{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:40:24Z","timestamp":1776786024411,"version":"3.51.2"},"reference-count":26,"publisher":"American Mathematical Society (AMS)","issue":"257","license":[{"start":{"date-parts":[[2007,8,8]],"date-time":"2007-08-08T00:00:00Z","timestamp":1186531200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We introduce the Shepard\u2013Bernoulli operator as a combination of the Shepard operator with a new univariate interpolation operator: the generalized Taylor polynomial. Some properties and the rate of convergence of the new combined operator are studied and compared with those given for classical combined Shepard operators. An application to the interpolation of discrete solutions of initial value problems is given.<\/p>","DOI":"10.1090\/s0025-5718-06-01894-1","type":"journal-article","created":{"date-parts":[[2006,11,1]],"date-time":"2006-11-01T16:50:02Z","timestamp":1162399802000},"page":"299-321","source":"Crossref","is-referenced-by-count":32,"title":["Shepard\u2013Bernoulli operators"],"prefix":"10.1090","volume":"76","author":[{"given":"R.","family":"Caira","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"F.","family":"Dell\u2019Accio","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2006,8,8]]},"reference":[{"key":"1","series-title":"A Wiley-Interscience Publication","isbn-type":"print","volume-title":"Handbook of mathematical functions with formulas, graphs, and mathematical tables","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/0471800074"},{"key":"2","series-title":"Mathematics and its Applications","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-011-2026-5","volume-title":"Error inequalities in polynomial interpolation and their applications","volume":"262","author":"Agarwal, Ravi P.","year":"1993","ISBN":"https:\/\/id.crossref.org\/isbn\/0792323378"},{"key":"3","isbn-type":"print","volume-title":"An introduction to numerical analysis","author":"Atkinson, Kendall E.","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0471029858"},{"key":"4","isbn-type":"print","first-page":"69","article-title":"Representation and approximation of surfaces","author":"Barnhill, Robert E.","year":"1977","ISBN":"https:\/\/id.crossref.org\/isbn\/0125872607"},{"issue":"1-2","key":"5","first-page":"33","article-title":"Hermite-type Shepard operators","volume":"26","author":"Coman, Gheorghe","year":"1997","journal-title":"Rev. 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