{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T17:40:15Z","timestamp":1776793215914,"version":"3.51.2"},"reference-count":22,"publisher":"American Mathematical Society (AMS)","issue":"274","license":[{"start":{"date-parts":[[2011,11,5]],"date-time":"2011-11-05T00:00:00Z","timestamp":1320451200000},"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>\n                    This paper presents a new nonlinear dyadic subdivision scheme eliminating the Gibbs oscillations close to discontinuities. Its convergence, stability and order of approximation are analyzed. It is proved that this scheme converges towards limit functions H\u00f6lder continuous with exponent larger than\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1.299\">\n                        <mml:semantics>\n                          <mml:mn>1.299<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">1.299<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Numerical estimates provide a H\u00f6lder exponent of\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"2.438\">\n                        <mml:semantics>\n                          <mml:mn>2.438<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">2.438<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . This subdivision scheme is the first one that simultaneously achieves the control of the Gibbs phenomenon and has limit functions with H\u00f6lder exponent larger than\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"1\">\n                        <mml:semantics>\n                          <mml:mn>1<\/mml:mn>\n                          <mml:annotation encoding=\"application\/x-tex\">1<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    .\n                  <\/p>","DOI":"10.1090\/s0025-5718-2010-02434-2","type":"journal-article","created":{"date-parts":[[2010,12,29]],"date-time":"2010-12-29T14:39:49Z","timestamp":1293633589000},"page":"959-971","source":"Crossref","is-referenced-by-count":20,"title":["On a nonlinear subdivision scheme avoiding Gibbs oscillations and converging towards \ud835\udc36^{\ud835\udc60} functions with \ud835\udc60&gt;1"],"prefix":"10.1090","volume":"80","author":[{"given":"S.","family":"Amat","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"K.","family":"Dadourian","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Liandrat","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2010,11,5]]},"reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"Amat S., Ar\u00e0ndiga F., Cohen A. and Donat R., (2002). 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