{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T10:44:29Z","timestamp":1778496269176,"version":"3.51.4"},"reference-count":36,"publisher":"American Mathematical Society (AMS)","issue":"330","license":[{"start":{"date-parts":[[2022,4,23]],"date-time":"2022-04-23T00:00:00Z","timestamp":1650672000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100003130","name":"Fonds Wetenschappelijk Onderzoek","doi-asserted-by":"publisher","award":["G091920N"],"award-info":[{"award-number":["G091920N"]}],"id":[{"id":"10.13039\/501100003130","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We consider rank-\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                    lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fourier space and the non-periodic cosine space and Chebyshev space, via tent transform and then cosine transform, to transfer known results from the periodic setting into new insights for the non-periodic settings. Fast discrete cosine transform can be applied for the reconstruction phase. To reduce the size of the auxiliary index set in the associated component-by-component (CBC) construction for the lattice generating vectors, we work with a bi-orthonormal set of basis functions, leading to three methods for function reconstruction in the non-periodic settings. We provide new theory and efficient algorithmic strategies for the CBC construction. We also interpret our results in the context of general function approximation and discrete least-squares approximation.\n                  <\/p>","DOI":"10.1090\/mcom\/3595","type":"journal-article","created":{"date-parts":[[2021,4,14]],"date-time":"2021-04-14T16:24:18Z","timestamp":1618417458000},"page":"1861-1897","source":"Crossref","is-referenced-by-count":18,"title":["Function integration, reconstruction and approximation using rank-1 lattices"],"prefix":"10.1090","volume":"90","author":[{"given":"Frances","family":"Kuo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Giovanni","family":"Migliorati","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabio","family":"Nobile","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dirk","family":"Nuyens","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2021,4,23]]},"reference":[{"issue":"4","key":"1","doi-asserted-by":"publisher","first-page":"993","DOI":"10.1007\/s00211-016-0861-7","article-title":"Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness","volume":"136","author":"Byrenheid, Glenn","year":"2017","journal-title":"Numer. 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