{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:03:32Z","timestamp":1760144612939,"version":"build-2065373602"},"reference-count":17,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T00:00:00Z","timestamp":1715558400000},"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>Quasi-interpolation is a powerful tool for approximating functions using radial basis functions (RBFs) such as Gaussian kernels. This avoids solving large systems of equations as in RBF interpolation. However, quasi-interpolation with Gaussian kernels on compact intervals can have significant errors near the boundaries. This paper proposes a quasi-interpolation method with Gaussian kernels using Chebyshev points and boundary corrections to improve the approximation near the boundaries. The boundary corrections use a linear approximation of the function beyond the interval to estimate the truncation error and add correction terms. Numerical studies on test functions show that the proposed method reduces errors significantly near boundaries compared to quasi-interpolation without corrections, for both equally spaced and Chebyshev points. The convergence and accuracy with the boundary corrections are generally better with Chebyshev points compared to equally spaced points. The proposed method provides an efficient way to perform quasi-interpolation on compact intervals while controlling the boundary errors. This study introduces a novel approach to quasi-interpolation modification, which significantly enhances convergence rates and minimizes errors at boundary points, thereby advancing the methods for boundary approximation.<\/jats:p>","DOI":"10.3390\/computation12050100","type":"journal-article","created":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T08:33:03Z","timestamp":1715589183000},"page":"100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Quasi-Interpolation on Chebyshev Grids with Boundary Corrections"],"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":[[2024,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Wendland, H. (2004). Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press.","DOI":"10.1017\/CBO9780511617539"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Buhmann, M. (2003). Radial Basis Functions: Theory and Implementations. Radial Basis Funct., 12.","DOI":"10.1017\/CBO9780511543241"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"891","DOI":"10.1016\/S0898-1221(03)90151-9","article-title":"A numerical study of some radial basis function based solution methods for elliptic PDEs","volume":"46","author":"Larsson","year":"2003","journal-title":"Comput. Math. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.jbi.2014.03.008","article-title":"A medical diagnostic tool based on radial basis function classifiers and evolutionary simulated annealing","volume":"49","author":"Alexandridis","year":"2014","journal-title":"J. Biomed. 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Dell\u2019Universita\u2019Di Ferrara"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1093\/imanum\/16.1.13","article-title":"On approximate approximations using Gaussian kernels","volume":"16","author":"Schmidt","year":"1996","journal-title":"IMA J. Numer. Anal."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.jat.2006.08.004","article-title":"Error estimates for approximate approximations with gaussian kernels on compact intervals","volume":"145","author":"Muller","year":"2007","journal-title":"J. Approx. Theory"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Cheney, E., and Light, W. (2009). A Course in Approximation Theory, American Mathematical Society. Graduate Studies in Mathematics.","DOI":"10.1090\/gsm\/101"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Mason, J.C., and Handscomb, D. (2003). Chebyshev Polynomials, Chapman & Hall\/CRC.","DOI":"10.1201\/9781420036114"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2934","DOI":"10.1093\/imanum\/drac059","article-title":"Multilevel quasi-interpolation","volume":"43","author":"Franz","year":"2023","journal-title":"IMA J. Numer. Anal."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Ern, A., Guermond, J.L., Ern, A., and Guermond, J.L. (2021). Finite Elements I: Approximation and Interpolation, Springer.","DOI":"10.1007\/978-3-030-56341-7"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/5\/100\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:41:24Z","timestamp":1760107284000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/5\/100"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,13]]},"references-count":17,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["computation12050100"],"URL":"https:\/\/doi.org\/10.3390\/computation12050100","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2024,5,13]]}}}