Local derivative estimation for scattered data interpolation
Applied Mathematics and Computation
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
Error estimates for modified local Shepard's interpolation formula
Applied Numerical Mathematics
On derivative estimation and the solution of least squares problems
Journal of Computational and Applied Mathematics
| Hi-index | 0.01 |
Least squares gradient estimates find application in many fields of computational science, particularly for the purposes of surface fitting and gradient reconstruction in computational fluid dynamics and data visualization. In this paper we derive error bounds for classical and weighted least squares gradient estimates. The bounds reflect how the number of points used in the least squares stencil and the smallest singular value of the least squares matrix impact the accuracy of these estimates. We show how an extrapolation method based on Householder transformations provides substantially tighter bounds. Numerical case studies are presented to elucidate our theory for a data set taken from Franke [Math. Comp., 38 (1982), pp. 181-200].