The aim of this paper is to provide a fast method, with a good quality of reproduction, to recover functions from very large and irregularly scattered samples of noisy data, which may present outliers. To the given sample of size N, we associate a uniform grid and, around each grid point, we condense the local information given by the noisy data by a suitable estimator. The recovering is then performed by a stable interpolation based on isotropic polyharmonic B-splines. Due to the good approximation rate, we need only M ≪ N degrees of freedom to recover the phenomenon faithfully. © 2010 Elsevier Inc. All rights reserved.
Bozzini, M., Lenarduzzi, L., Rossini, M. (2010). Polyharmonic splines: an approximation method for noisy scattered data of extra large size. APPLIED MATHEMATICS AND COMPUTATION, 216(1), 317-331 [10.1016/j.amc.2010.01.065].
Polyharmonic splines: an approximation method for noisy scattered data of extra large size
BOZZINI, MARIA TUGOMIRA;ROSSINI, MILVIA FRANCESCA
2010
Abstract
The aim of this paper is to provide a fast method, with a good quality of reproduction, to recover functions from very large and irregularly scattered samples of noisy data, which may present outliers. To the given sample of size N, we associate a uniform grid and, around each grid point, we condense the local information given by the noisy data by a suitable estimator. The recovering is then performed by a stable interpolation based on isotropic polyharmonic B-splines. Due to the good approximation rate, we need only M ≪ N degrees of freedom to recover the phenomenon faithfully. © 2010 Elsevier Inc. All rights reserved.
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