Multivariate data-dependent partition of unity based on Moving Least Squares method

Inmaculada Garcés, Juan Ruiz-Álvarez and Dionisio F. Yáñez

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 245, issue C, 610-627

Abstract: Data approximation is essential in fields such as geometric design, numerical PDEs, and curve modeling. Moving Least Squares (MLS) is a widely used method for data fitting; however, its accuracy degrades in the presence of discontinuities, often resulting in spurious oscillations similar to those associated with the Gibbs phenomenon. This work extends the integration of MLS with the Weighted Essentially Non-Oscillatory (WENO) method and with an innovative partition of unity approach to higher dimensions. We propose a data-dependent operator using the novel Non-Linear Partition of Unity based on Moving Least Squares method in Rn, which improves accuracy near discontinuities and maintains high-order accuracy in smooth regions. We demonstrate some theoretical properties of the method and perform numerical experiments to validate its effectiveness.

Keywords: MLS; PUM; WENO; High accuracy approximation; Improved adaptation to discontinuities; 41A05; 41A10; 65D05; 65M06; 65N06 (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:245:y:2026:i:c:p:610-627

DOI: 10.1016/j.matcom.2026.02.024

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