Interpolation and approximation of 3-D and 4-D scattered data

Scattered data approximation of fully fuzzy data by quasi-interpolation

Fuzzy quasi-interpolations help to reduce the complexity of solving a linear system of equations compared with fuzzy interpolations. Almost all fuzzy quasi-interpolations are focused on the form of $widetilde{f}^{*}:mathbb{R}rightarrow F(mathbb{R})$ or $widetilde{f}^{*}:F(mathbb{R})rightarrow mathbb{R}$.  In this paper, we intend to offer a novel fuzzy radial basis function by the concept of so...

3 D Terrain Reconstruction Using Scattered Data Sets

Hierarchical Matrix Approximation for Kernel-Based Scattered Data Interpolation

Scattered data interpolation by radial kernel functions leads to linear equation systems with large, fully populated, ill-conditioned interpolation matrices. A successful iterative solution of such a system requires an efficient matrix-vector multiplication as well as an efficient preconditioner. While multipole approaches provide a fast matrix-vector multiplication, they avoid the explicit set...

Scattered data interpolation by bivariate splines with higher approximation order

Given a set of scattered data, we usually use a minimal energy method to find Lagrange interpolation based on bivariate spline spaces over a triangulation of the scattered data locations. It is known that the approximation order of the minimal energy spline interpolation is only 2 in terms of the size of triangulation. To improve this order of approximation, we propose several new schemes in th...

The interpolation of a 3-D data set by a pair of 2-D filters

Seismic 3-D field data is often recorded as a set of relatively sparse and often irregular 2-D lines. Under the assumption that the data consists of the superposition of local plane waves, such data can be interpolated by prediction-error techniques using a set of two 2-D filters instead of the conventional single 3-D filter. The two 2-D prediction-error filters are found by two independent lin...