{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:25:52Z","timestamp":1760149552094,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T00:00:00Z","timestamp":1692662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Universiti Malaysia Sabah Press (UMS Press)","award":["UMS\/PPI-DPJ1"],"award-info":[{"award-number":["UMS\/PPI-DPJ1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper presents the advanced classes of linear symmetric subdivision schemes for the fitting of data and the creation of geometric shapes. These schemes are derived from the B-spline and Lagrange\u2019s blending functions. The important characteristics of the derived schemes, including continuity, support, and the impact of parameters on the magnitude of the artifact and Gibbs oscillations are discussed. Schemes additionally generalize various subdivision schemes. Linear symmetric subdivision schemes can produce Gibbs oscillations when the initial data is taken from discontinuous functions. Additionally, these schemes may generate unwanted artifacts in the limit curve that do not exist in the original polygon. One solution is to use non-linear schemes, but this approach increases the computational complexity of the scheme. An alternative approach is proposed that involves modifying the linear symmetric schemes by introducing parameters into the linear rules. The suitable values of these parameters reduce or eliminate Gibbs oscillations and artifacts while still using linear symmetric schemes. Our approach provides a balance between reducing or eliminating Gibbs oscillations and artifacts while maintaining computational efficiency.<\/jats:p>","DOI":"10.3390\/sym15091620","type":"journal-article","created":{"date-parts":[[2023,8,22]],"date-time":"2023-08-22T08:58:54Z","timestamp":1692694734000},"page":"1620","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Generalized Classes of Linear Symmetric Subdivision Schemes Free from Gibbs Oscillations and Artifacts in the Fitting of Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6518-6705","authenticated-orcid":false,"given":"Samsul Ariffin Abdul","family":"Karim","sequence":"first","affiliation":[{"name":"Software Engineering Programme, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Malaysia"},{"name":"Data Technologies and Applications (DaTA) Research Lab, Faculty of Computing and Informatics, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Malaysia"},{"name":"Creative Advanced Machine Intelligence (CAMI) Research Centre, Universiti Malaysia Sabah, Jalan UMS, Kota Kinabalu 88400, Malaysia"}]},{"given":"Rakib","family":"Mustafa","sequence":"additional","affiliation":[{"name":"Department of Computer System Engineering, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6772-2441","authenticated-orcid":false,"given":"Humaira Mustanira","family":"Tariq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0441-8485","authenticated-orcid":false,"given":"Ghulam","family":"Mustafa","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4246-8253","authenticated-orcid":false,"given":"Rabia","family":"Hameed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Government Sadiq College Women University, Bahawalpur 63100, Pakistan"}]},{"given":"Sidra","family":"Razaq","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,22]]},"reference":[{"key":"ref_1","unstructured":"Dyn, N., Floater, M., and Hormann, K. 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