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)
Multivariate vertex splines and finite elements
Journal of Approximation Theory
Algorithm 792: accuracy test of ACM algorithms for interpolation of scattered data in the plane
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
Multi-node higher order expansions of a function
Journal of Approximation Theory
Error estimates for modified local Shepard's interpolation formula
Applied Numerical Mathematics
Multivariate approximation by a combination of modified Taylor polynomials
Journal of Computational and Applied Mathematics
Increasing the polynomial reproduction of a quasi-interpolation operator
Journal of Approximation Theory
An asymptotic expansion for the error in a linear map that reproduces polynomials of a certain order
Journal of Approximation Theory
On the bivariate Shepard-Lidstone operators
Journal of Computational and Applied Mathematics
A meshless interpolation algorithm using a cell-based searching procedure
Computers & Mathematics with Applications
| Hi-index | 0.09 |
We show how to combine local Shepard operators with Hermite polynomials on the simplex [C. K. Chui, M.-J. Lai, Multivariate vertex splines and finite elements, J. Approx. Theory 60 (1990) 245-343] so as to raise the algebraic precision of the Shepard-Taylor operators [R. Farwig, Rate of convergence of Shepard's global interpolation formula, Math. Comp. 46 (1986) 577-590] that use the same data and contemporaneously maintain the interpolation properties at each sample point (derivative data included) and a good accuracy of approximation. Numerical results are provided.