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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