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Our main motivation is the influential paper [4]. We repeat and extend their theoretical analysis and numerical experiments for SA and compare them to LS in dimensions up to 100. Our extensive experiments demonstrate that LS, even with only slight oversampling, consistently matches the accuracy of SA in low dimensions. In high dimensions, however, LS shows clear superiority.\n                  <\/jats:p>","DOI":"10.1007\/s10444-026-10316-5","type":"journal-article","created":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T08:40:55Z","timestamp":1780389655000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sparse grids vs. random points for high-dimensional polynomial approximation"],"prefix":"10.1007","volume":"52","author":[{"given":"Jakob","family":"Eggl","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Elias","family":"Mindlberger","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1120-8467","authenticated-orcid":false,"given":"Mario","family":"Ullrich","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,6,2]]},"reference":[{"key":"10316_CR1","doi-asserted-by":"publisher","unstructured":"Anderson, E., Bai, Z., Bischof, C., et al.: LAPACK users\u2019 guide. 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