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The paper gives a full error analysis, and full details of the construction of lattices needed to ensure a good (but inevitably not optimal) rate of convergence and an error bound independent of dimension. Numerical experiments support the theory.<\/jats:p>","DOI":"10.1007\/s00211-021-01242-3","type":"journal-article","created":{"date-parts":[[2021,11,30]],"date-time":"2021-11-30T18:58:19Z","timestamp":1638298699000},"page":"33-77","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Fast approximation by periodic kernel-based lattice-point interpolation with application in uncertainty quantification"],"prefix":"10.1007","volume":"150","author":[{"given":"Vesa","family":"Kaarnioja","sequence":"first","affiliation":[]},{"given":"Yoshihito","family":"Kazashi","sequence":"additional","affiliation":[]},{"given":"Frances Y.","family":"Kuo","sequence":"additional","affiliation":[]},{"given":"Fabio","family":"Nobile","sequence":"additional","affiliation":[]},{"given":"Ian H.","family":"Sloan","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,30]]},"reference":[{"key":"1242_CR1","doi-asserted-by":"publisher","first-page":"993","DOI":"10.1007\/s00211-016-0861-7","volume":"136","author":"G Byrenheid","year":"2017","unstructured":"Byrenheid, G., K\u00e4mmerer, L., Ullrich, T., Volkmer, T.: Tight error bounds for rank-$$1$$ lattice sampling in spaces of hybrid mixed smoothness. 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