{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T04:12:13Z","timestamp":1648959133479},"reference-count":5,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,12,1]],"date-time":"2012-12-01T00:00:00Z","timestamp":1354320000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>S<\/jats:italic><jats:sub>1<\/jats:sub>=<jats:italic>S<\/jats:italic><jats:sub>1<\/jats:sub>(<jats:italic>v<\/jats:italic><jats:sub>0<\/jats:sub>,\u2026,<jats:italic>v<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic>+1<\/jats:sub>) be the space of compactly supported <jats:italic>C<\/jats:italic><jats:sup>0<\/jats:sup> piecewise linear functions on a mesh <jats:italic>M<\/jats:italic> of lines through \u2124<jats:sup>2<\/jats:sup> in directions <jats:italic>v<\/jats:italic><jats:sub>0<\/jats:sub>,\u2026,<jats:italic>v<\/jats:italic><jats:sub><jats:italic>r<\/jats:italic>+1<\/jats:sub>, possibly satisfying some restrictions on the jumps of the first order derivative. A sequence \u03d5=(\u03d5<jats:sub>1<\/jats:sub>,\u2026,\u03d5<jats:sub><jats:italic>r<\/jats:italic><\/jats:sub>) of elements of <jats:italic>S<\/jats:italic><jats:sub>1<\/jats:sub> is called a multi-box spline if every element of <jats:italic>S<\/jats:italic><jats:sub>1<\/jats:sub> is a finite linear combination of shifts of (the components of) \u03d5. We give some examples for multi-box splines and show that they are stable. It is further shown that any multi-box spline is not always symmetric<\/jats:p>","DOI":"10.1112\/s1461157012001167","type":"journal-article","created":{"date-parts":[[2013,1,7]],"date-time":"2013-01-07T14:01:05Z","timestamp":1357567265000},"page":"444-462","source":"Crossref","is-referenced-by-count":0,"title":["Examples of linear multi-box splines"],"prefix":"10.1112","volume":"15","author":[{"given":"Abdellatif","family":"Bettayeb","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,12,1]]},"reference":[{"key":"S1461157012001167_ref2","first-page":"125","volume-title":"Advanced topics in multivariate approximation","author":"Goodman","year":"1996"},{"key":"S1461157012001167_ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00365-006-0654-3"},{"key":"S1461157012001167_ref3","first-page":"151","volume-title":"Surface fitting and multiresolution methods","author":"Goodman","year":"1997"},{"key":"S1461157012001167_ref4","first-page":"55","volume-title":"Topics in Multivariate Approximation and Interpolation","author":"Goodman","year":"2005"},{"key":"S1461157012001167_ref1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00373-3"}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157012001167","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T00:46:52Z","timestamp":1559868412000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157012001167\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,12,1]]},"references-count":5,"alternative-id":["S1461157012001167"],"URL":"https:\/\/doi.org\/10.1112\/s1461157012001167","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,12,1]]}}}