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The recently proposed\n                    <jats:italic>tensor product multilevel method (TPML)<\/jats:italic>\n                    combines Smolyak\u2019s sparse grid method with a kernel-based residual correction technique. The contributions of this paper are twofold. First, we present two improvements on the TPML that reduce the computational cost of point evaluations compared to a naive implementation. Second, we provide numerical examples that demonstrate the effectiveness and innovation of the TPML.\n                  <\/jats:p>","DOI":"10.1007\/s10915-025-03144-0","type":"journal-article","created":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T04:54:48Z","timestamp":1764651288000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Numerical Aspects of the Tensor Product Multilevel Method for High-Dimensional, Kernel-Based Reconstruction on Sparse Grids"],"prefix":"10.1007","volume":"106","author":[{"given":"Markus","family":"B\u00fcttner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-5040-0569","authenticated-orcid":false,"given":"R\u00fcdiger","family":"Kempf","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Holger","family":"Wendland","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,12,2]]},"reference":[{"key":"3144_CR1","first-page":"1042","volume":"148","author":"SA Smoljak","year":"1963","unstructured":"Smoljak, S.A.: Quadrature and interpolation formulae on tensor products of certain function classes. 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