{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:17:28Z","timestamp":1760145448147,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T00:00:00Z","timestamp":1721260800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper investigates the potential of utilising multilevel quasi-interpolation techniques on Chebyshev sparse grids for complex numerical computations. The paper starts by laying down the motivations for choosing Chebyshev sparse grids and quasi-interpolation methods with Gaussian kernels. It delves into the practical aspects of implementing these techniques. Various numerical experiments are performed to evaluate the efficiency and limitations of the multilevel quasi-sparse interpolation methods with dimensions two dimension and three dimension. The work ultimately aims to provide a comprehensive understanding of the computational efficiency and accuracy achievable through this approach, comparing its performance with traditional methods.<\/jats:p>","DOI":"10.3390\/computation12070149","type":"journal-article","created":{"date-parts":[[2024,7,18]],"date-time":"2024-07-18T14:59:50Z","timestamp":1721314790000},"page":"149","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multilevel Quasi-Interpolation on Chebyshev Sparse Grids"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-3428-9946","authenticated-orcid":false,"given":"Faisal","family":"Alsharif","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah 30002, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,18]]},"reference":[{"key":"ref_1","unstructured":"Alsharif, F. 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Meshfree Approximation Methods with MATLAB of Interdisciplinary Mathematical Sciences, World Scientific Publishing Co. Pte. Ltd.","DOI":"10.1142\/6437"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1016\/j.jat.2009.08.004","article-title":"Error bounds for anisotropic rbf interpolation","volume":"162","author":"Beatson","year":"2010","journal-title":"J. Approx. Theory"},{"key":"ref_14","first-page":"1050","article-title":"The regularizing properties of anisotropic radial basis functions","volume":"190","author":"Casciola","year":"2007","journal-title":"Appl. Math. Comput."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/7\/149\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:19:08Z","timestamp":1760109548000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/7\/149"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,7,18]]},"references-count":14,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2024,7]]}},"alternative-id":["computation12070149"],"URL":"https:\/\/doi.org\/10.3390\/computation12070149","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2024,7,18]]}}}