Multivariate interpolation of large sets of scattered data
ACM Transactions on Mathematical Software (TOMS)
Sampling with Hammersley and Halton points
Journal of Graphics Tools
Algorithm 792: accuracy test of ACM algorithms for interpolation of scattered data in the plane
ACM Transactions on Mathematical Software (TOMS)
Least squares surface approximation using multiquadrics and parametric domain distortion
Computer Aided Geometric Design
Algorithm 798: high-dimensional interpolation using the modified Shepard method
ACM Transactions on Mathematical Software (TOMS)
Algorithm 660: QSHEP2D: Quadratic Shepard Method for Bivariate Interpolation of Scattered Data
ACM Transactions on Mathematical Software (TOMS)
Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
SIAM Journal on Scientific Computing
Radial basis functions for the multivariate interpolation of large scattered data sets
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
Meshfree Approximation Methods with MATLAB
Meshfree Approximation Methods with MATLAB
Stable computation of multiquadric interpolants for all values of the shape parameter
Computers & Mathematics with Applications
Fast and accurate interpolation of large scattered data sets on the sphere
Journal of Computational and Applied Mathematics
Algorithm 905: SHEPPACK: Modified Shepard Algorithm for Interpolation of Scattered Multivariate Data
ACM Transactions on Mathematical Software (TOMS)
Stable Computations with Gaussian Radial Basis Functions
SIAM Journal on Scientific Computing
Multivariate interpolation with increasingly flat radial basis functions of finite smoothness
Advances in Computational Mathematics
Stable Evaluation of Gaussian Radial Basis Function Interpolants
SIAM Journal on Scientific Computing
Enhancing the approximation order of local Shepard operators by Hermite polynomials
Computers & Mathematics with Applications
Numerical integration on multivariate scattered data by Lobachevsky splines
International Journal of Computer Mathematics
Error estimates and condition numbers for radial basis function interpolation
Advances in Computational Mathematics
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In this paper we propose a fast algorithm for bivariate interpolation of large scattered data sets. It is based on the partition of unity method for constructing a global interpolant by blending radial basis functions as local approximants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cell-based searching procedure. More precisely, we construct a cell structure, which partitions the domain and strictly depends on the dimension of the subdomains, thus providing a meaningful improvement in the searching process compared to the nearest neighbour searching techniques presented in Allasia et al. (2011) and Cavoretto and De Rossi (2010, 2012). In fact, this efficient algorithm and, in particular, the new searching procedure enable us a fast computation also in several applications, where the amount of data to be interpolated is often very large, up to many thousands or even millions of points. Analysis of computational complexity shows the high efficiency of the proposed interpolation algorithm. This is also supported by numerical experiments.