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

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Title: Multivariate data-dependent partition of unity based on Moving Least Squares method.
Authors: Garcés, Inmaculada1,2 (AUTHOR) inmaculada.garces@uv.es, Ruiz-Álvarez, Juan3 (AUTHOR) juan.ruiz@upct.es, Yáñez, Dionisio F.2 (AUTHOR) dionisio.yanez@uv.es
Source: Mathematics & Computers in Simulation. Jul2026, Vol. 245, p610-627. 18p.
Subjects: Partition of unity method, Least squares, Discontinuous functions, Curve fitting, Iterative methods (Mathematics), Numerical solutions to partial differential equations
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 R n , 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. [ABSTRACT FROM AUTHOR]
Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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DbLabel: Engineering Source
An: 192483792
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  Data: Multivariate data-dependent partition of unity based on Moving Least Squares method.
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  Data: <searchLink fieldCode="JN" term="%22Mathematics+%26+Computers+in+Simulation%22">Mathematics & Computers in Simulation</searchLink>. Jul2026, Vol. 245, p610-627. 18p.
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  Data: <searchLink fieldCode="DE" term="%22Partition+of+unity+method%22">Partition of unity method</searchLink><br /><searchLink fieldCode="DE" term="%22Least+squares%22">Least squares</searchLink><br /><searchLink fieldCode="DE" term="%22Discontinuous+functions%22">Discontinuous functions</searchLink><br /><searchLink fieldCode="DE" term="%22Curve+fitting%22">Curve fitting</searchLink><br /><searchLink fieldCode="DE" term="%22Iterative+methods+%28Mathematics%29%22">Iterative methods (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+to+partial+differential+equations%22">Numerical solutions to partial differential equations</searchLink>
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  Data: 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 R n , 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Mathematics & Computers in Simulation is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1016/j.matcom.2026.02.024
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      – Code: eng
        Text: English
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        PageCount: 18
        StartPage: 610
    Subjects:
      – SubjectFull: Partition of unity method
        Type: general
      – SubjectFull: Least squares
        Type: general
      – SubjectFull: Discontinuous functions
        Type: general
      – SubjectFull: Curve fitting
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Numerical solutions to partial differential equations
        Type: general
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      – TitleFull: Multivariate data-dependent partition of unity based on Moving Least Squares method.
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            NameFull: Ruiz-Álvarez, Juan
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            NameFull: Yáñez, Dionisio F.
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          Dates:
            – D: 01
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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