In this paper our concern is the recovery of a highly regular function by a discrete set of data with arbitrary distribution. We consider the case of a nonstationary multiquadric interpolant that presents numerical breakdown. Therefore we propose a global least squares multiquadric approximant with a center set of maximal size and obtained by a new thinning technique. The new thinning scheme removes the local bad conditions in order to obtain a well conditioned matrix. The choice of working on local subsets of the data set $X$ provides an effective solution. Some numerical examples to validate the goodness of our proposal are given.
Bozzini, M., Lenarduzzi, L. (2010). Stable multiquadric approximation by local thinning. In M.C.:P. Lopez de Silanes, G. Sanz, torrens J.J, M. Madaune-Tort, Parossin C, D. Rujillo (a cura di), Tenth International conference Zaragoza-Pau on Applied Mathematics and Statistics (pp. 73-82).
Stable multiquadric approximation by local thinning
BOZZINI, MARIA TUGOMIRA;
2010
Abstract
In this paper our concern is the recovery of a highly regular function by a discrete set of data with arbitrary distribution. We consider the case of a nonstationary multiquadric interpolant that presents numerical breakdown. Therefore we propose a global least squares multiquadric approximant with a center set of maximal size and obtained by a new thinning technique. The new thinning scheme removes the local bad conditions in order to obtain a well conditioned matrix. The choice of working on local subsets of the data set $X$ provides an effective solution. Some numerical examples to validate the goodness of our proposal are given.
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