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In the existing literature such problems are mainly addressed via the well-established<jats:italic>knot insertion<\/jats:italic>or<jats:italic>knot removal<\/jats:italic>schemes. Such iterative strategies are usually quite demanding from a computational point of view and our goal is to study an efficient implementation for data removal approaches, namely efficient reduced basis algorithm (ERBA). Focusing on kernel-based interpolation, the algorithm makes use of two iterative rules for removing data. The former, called ERBA-<jats:italic>r<\/jats:italic>, is based on classical residual evaluations. The latter, namely ERBA-<jats:italic>p<\/jats:italic>, is independent of the function values and relies on error bounds defined by the power function. In both cases, inspired by the so-called extended Rippa\u2019s algorithm, our ERBA takes advantage of a fast implementation.<\/jats:p>","DOI":"10.1007\/s10915-022-01818-7","type":"journal-article","created":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T02:05:32Z","timestamp":1648519532000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Efficient Reduced Basis Algorithm (ERBA) for Kernel-Based Approximation"],"prefix":"10.1007","volume":"91","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1087-7589","authenticated-orcid":false,"given":"Francesco","family":"Marchetti","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emma","family":"Perracchione","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,3,28]]},"reference":[{"key":"1818_CR1","doi-asserted-by":"publisher","DOI":"10.1142\/6437","volume-title":"Meshfree Approximations Methods with Matlab","author":"GE Fasshauer","year":"2007","unstructured":"Fasshauer, G.E.: Meshfree Approximations Methods with Matlab. 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