Rate of convergence of Shepard's global interpolation formula
Mathematics of Computation
Multivariate interpolation of large sets of scattered data
ACM Transactions on Mathematical Software (TOMS)
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Good quality point sets and error estimates for moving least square approximations
Applied Numerical Mathematics - Special issue on applied and computational mathematics: Selected papers of the fourth PanAmerican workshop
Multivariate approximation by a combination of modified Taylor polynomials
Journal of Computational and Applied Mathematics
Error Bounds for Least Squares Gradient Estimates
SIAM Journal on Scientific Computing
Enhancing the approximation order of local Shepard operators by Hermite polynomials
Computers & Mathematics with Applications
Complementary Lidstone interpolation on scattered data sets
Numerical Algorithms
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The aim of this paper is to obtain error estimates for a modified local Shepard's approximation. This interpolation operator uses approximated Taylor polynomials at the data points glued together by a local Shepard's partition of unity. We introduce a condition number which is a geometric measure of the quality of the approximate derivatives obtained by least square fits of polynomials to function values at nearby nodes. The condition number is practically computable and it is closely related to the approximating power of the method. The error estimates obtained are important in the analysis of Galerkin approximations based on these Shepard's interpolation operators.