{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:38:50Z","timestamp":1760243930107,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2010,7,30]],"date-time":"2010-07-30T00:00:00Z","timestamp":1280448000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>We analytically investigate univariate C1 continuous cubic L1 interpolating splines calculated by minimizing an L1 spline functional based on the second derivative on 5-point windows. Specifically, we link geometric properties of the data points in the windows with linearity, convexity and oscillation properties of the resulting L1 spline. These analytical results provide the basis for a computationally efficient algorithm for calculation of L1 splines on 5-point windows.<\/jats:p>","DOI":"10.3390\/a3030276","type":"journal-article","created":{"date-parts":[[2010,7,30]],"date-time":"2010-07-30T11:07:54Z","timestamp":1280488074000},"page":"276-293","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Univariate Cubic L1 Interpolating Splines: Analytical Results for Linearity, Convexity and Oscillation on 5-PointWindows"],"prefix":"10.3390","volume":"3","author":[{"given":"Qingwei","family":"Jin","sequence":"first","affiliation":[{"name":"Industrial and Systems Engineering Department, North Carolina State University, Raleigh, NC 27695-7906, USA"}]},{"given":"John E.","family":"Lavery","sequence":"additional","affiliation":[{"name":"Industrial and Systems Engineering Department, North Carolina State University, Raleigh, NC 27695-7906, USA"},{"name":"Mathematical Sciences Division, Army Research Office, Army Research Laboratory, P.O. Box 12211, Research Triangle Park, NC 27709-2211, USA"}]},{"given":"Shu-Cherng","family":"Fang","sequence":"additional","affiliation":[{"name":"Industrial and Systems Engineering Department, North Carolina State University, Raleigh, NC 27695-7906, USA"}]}],"member":"1968","published-online":{"date-parts":[[2010,7,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.cagd.2007.04.007","article-title":"C1 and C2-continuous polynomial parametric Lp splines (p \u2265 1)","volume":"24","author":"Auquiert","year":"2007","journal-title":"Comput. Aided Geom. Design"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s11075-007-9140-0","article-title":"On the cubic L1 spline interpolant to the Heaviside function","volume":"46","author":"Auquiert","year":"2007","journal-title":"Numer. Algorithms"},{"key":"ref_3","unstructured":"Bulatov, D., and Lavery, J.E. (, January February). 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Algorithms, in press.","DOI":"10.3390\/a3030311"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/3\/3\/276\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:03:02Z","timestamp":1760220182000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/3\/3\/276"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,30]]},"references-count":25,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2010,9]]}},"alternative-id":["a3030276"],"URL":"https:\/\/doi.org\/10.3390\/a3030276","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2010,7,30]]}}}