{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T15:23:28Z","timestamp":1648567408541},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advs. Complex Syst."],"published-print":{"date-parts":[[2006,9]]},"abstract":"<jats:p> Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R<jats:sup>2<\/jats:sup> or R<jats:sup>3<\/jats:sup> (R is the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended from R<jats:sup>3<\/jats:sup> to R<jats:sup>n<\/jats:sup> (n is an integer greater than 3), which is called the multi-dimensional piece-wise self-affine fractal interpolation model. <\/jats:p><jats:p> This model uses a \"mapping partial derivative\" and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine in R<jats:sup>n<\/jats:sup>. Therefore, the result is very general. Moreover, the multi-dimensional piece-wise self-affine fractal interpolation model in tensor form is more terse than in the usual matrix form. <\/jats:p>","DOI":"10.1142\/s0219525906000756","type":"journal-article","created":{"date-parts":[[2006,12,5]],"date-time":"2006-12-05T11:52:44Z","timestamp":1165319564000},"page":"287-293","source":"Crossref","is-referenced-by-count":3,"title":["MULTI-DIMENSIONAL PIECE-WISE SELF-AFFINE FRACTAL INTERPOLATION MODEL IN TENSOR FORM"],"prefix":"10.1142","volume":"09","author":[{"given":"TONG","family":"ZHANG","sequence":"first","affiliation":[{"name":"Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China"}]},{"given":"JIANLIN","family":"LIU","sequence":"additional","affiliation":[{"name":"Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China"}]},{"given":"ZHUO","family":"ZHUANG","sequence":"additional","affiliation":[{"name":"Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing, 100084, China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1109\/78.143444"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1109\/78.330394"},{"key":"rf4","doi-asserted-by":"crossref","unstructured":"M.\u00a0Peruggia, Discrete Iterated Function Systems (Wellesley, Massachusetts, 1993)\u00a0pp. 12\u201331.","DOI":"10.1201\/9781439864708"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1109\/10.915713"},{"key":"rf6","first-page":"207","volume":"54","author":"Craciunescu O. I.","journal-title":"Bioeng. Division (ASME)"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1088\/1741-2560\/2\/2\/002"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1209\/epl\/i2004-10383-2"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1137\/0520080"},{"key":"rf11","unstructured":"M. F.\u00a0Barnsley, Fractals Everywhere (Academic Press Professional, Boston, 1993)\u00a0p. 236."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.2514\/3.10593"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0165-1684(94)00100-E"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/BF01893434"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/BF01889596"}],"container-title":["Advances in Complex Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219525906000756","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T04:52:14Z","timestamp":1565153534000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219525906000756"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,9]]},"references-count":13,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,9]]}},"alternative-id":["10.1142\/S0219525906000756"],"URL":"https:\/\/doi.org\/10.1142\/s0219525906000756","relation":{},"ISSN":["0219-5259","1793-6802"],"issn-type":[{"value":"0219-5259","type":"print"},{"value":"1793-6802","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,9]]}}}