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Inspired by <jats:italic>hp<\/jats:italic>-approximation techniques of Binev, we use the underlying tree structure of the frame elements to derive an adaptive algorithm that, under standard assumptions concerning the local errors, can be used to create approximations with an error close to the best tree approximation error for a given cardinality. We support our findings by numerical experiments demonstrating that this approach can be used to achieve inverse-exponential convergence rates.<\/jats:p>","DOI":"10.1007\/s10444-024-10205-9","type":"journal-article","created":{"date-parts":[[2024,10,31]],"date-time":"2024-10-31T09:03:52Z","timestamp":1730365432000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Adaptive quarklet tree approximation"],"prefix":"10.1007","volume":"50","author":[{"given":"Stephan","family":"Dahlke","sequence":"first","affiliation":[]},{"given":"Marc","family":"Hovemann","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2607-3115","authenticated-orcid":false,"given":"Thorsten","family":"Raasch","sequence":"additional","affiliation":[]},{"given":"Dorian","family":"Vogel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,10,31]]},"reference":[{"issue":"4","key":"10205_CR1","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1137\/1036141","volume":"36","author":"I Babu\u0161ka","year":"1994","unstructured":"Babu\u0161ka, I., Suri, M.: The p- and h-p versions of the finite element method, basic principles and properties. 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