{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:24:11Z","timestamp":1787329451437,"version":"build-2736575974"},"reference-count":8,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>The hp-adaptive approximation is formulated as an approximation problem on a full binary tree $T$, where for each of the leaves $\\Delta$ an order $p(\\Delta)\\ge1$ is assigned in such a way that the sum of all orders $p(\\Delta)$ does not exceed $N$, which is called the complexity of the approximation. The leaves $\\Delta$ correspond to the cells of the partition, while $p(\\Delta)$ is the dimension of the polynomial space used for the local approximation on $\\Delta$. Devising an incremental algorithm for near-best adaptive approximation for the problem of finding the best possible tree $T$ and assignments $p(\\Delta)$ leads to building a construction that attaches a ghost tree with $p(\\Delta)$ leaves to each leaf $\\Delta$ of $T$ with $p(\\Delta)&gt;1$. The resulting full binary tree $\\mathcal{T}$ has at most $N$ leaves and can be used as a proxy of $T$ for assembling hp-adaptive procedures. Under the standard assumptions about the local errors, we prove that the error of our approximation of complexity $N$ is bounded by $\\frac{2N-1}{N-n+1}\\sigma_n$, where $\\sigma_n$, $n\\le N$, is the error of the best possible approximation of complexity $n$.<\/jats:p>","DOI":"10.1137\/18m1175070","type":"journal-article","created":{"date-parts":[[2018,11,29]],"date-time":"2018-11-29T11:18:02Z","timestamp":1543490282000},"page":"3346-3357","source":"Crossref","is-referenced-by-count":14,"title":["Tree Approximation for hp-Adaptivity"],"prefix":"10.1137","volume":"56","author":[{"given":"Peter","family":"Binev","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,11,29]]},"reference":[{"key":"atypb1","first-page":"1669","volume":"29","author":"Binev P.","year":"2007","journal-title":"Oberwolfach Rep."},{"key":"atypb2","first-page":"2192","volume":"39","author":"Binev P.","year":"2013","journal-title":"Oberwolfach Rep."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-003-0492-7"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-003-0493-6"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-19800-2_4"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1007\/s00211-016-0826-x"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2017.02.035"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2018.05.034"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1175070","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:18:03Z","timestamp":1787325483000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1175070"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":8,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/18M1175070"],"URL":"https:\/\/doi.org\/10.1137\/18m1175070","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}