10 papers
Adaptive Non-Linear Partition of Unity Methods for Scattered Data Interpolation with Discontinuities
Adeeba Haider, Roberto Cavoretto, Juan Ruiz-Ãlvarez +1
Scattered data approximation with discontinuities is challenging due to the Gibbs phenomenon, which significantly reduces accuracy near interfaces. The recently introduced Non-Line…
Data dependent Shepard approximation through and adaptive modification of the shape parameter
José Kuruc, Juan Ruiz-Ãlvarez, Bo Wang +1
In this article, we introduce a novel data-dependent Shepard interpolation method inspired by the adaptive strategies proposed in [2]. In this case, as Shepard interpolation does n…
A Cell-Average Non-Separable Progressive Multivariate WENO Method for Image Processing Applications
Inmaculada Garcés, Pep Mulet, Juan Ruiz-Ãlvarez +2
Accurate and efficient reconstruction techniques are essential in multiresolution analysis and image compression, particularly when the data are represented as cell averages. In th…
Multivariate Data-dependent Partition of Unity based on Moving Least Squares method
Inmaculada Garcés, Juan Ruiz-Ãlvarez, Dionisio F. Yáñez
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…
A general correction for numerical integration rules over piece-wise continuous functions
Shipra Mahata, Samala Rathan, Juan Ruiz-Ãlvarez +1
This article presents a novel approach to enhance the accuracy of classical quadrature rules by incorporating correction terms. The proposed method is particularly effective when t…
Integrating Moving Least Squares with non-linear WENO method: A novel Partition of Unity approach in 1D
Inmaculada Garcés, José M. Ramón, Juan Ruiz-Ãlvarez +1
The approximation of data is a fundamental challenge encountered in various fields, including computer-aided geometric design, the numerical solution of partial differential equati…