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We present a numerical method for the detection of faults and gradient faults of two dimensional functions when uniformly scattered and noisy data are given. The method recognizes the presence of a discontinuity curve by a suitable statistic. Moreover, we discuss the recovery of such curves and provide a computational bound for the pointwise error and convergence properties.

When the data are unevenly distributed and the behaviour of a function changes abruptly, the approximant can present undue oscillations. We present an algorithm to identify a domain decomposition, such that on each subdomain the behaviour of the function is sufficiently homogeneous in order to calculate separate approximants and to blend them together. © 2013 IMACS. Published by Elsevier B.V. All rights reserved.

The aim of the paper is to provide a computationally effective way to construct stable bases on general non-degenerate lattices. In particular, we define new stable bases on hexagonal lattices and we give some numerical examples which show their usefulness in applications.

Under very mild additional assumptions, translates of conditionally positive definite radial basis functions allow unique interpolation to scattered multivariate data, because the interpolation matrices have a symmetric and positive definite dominant part. In many applications, the data density varies locally according to the signal behaviour, and then the translates should get different scalings that match the local data density. Furthermore, if there is a local anisotropy in the data, the radial basis functions should possibly be distorted into functions with ellipsoids as level sets. In such cases, the symmetry and the definiteness of the matrices are no longer guaranteed. However, this brief note is the first paper to provide sufficient conditions for the unique solvability of such interpolation processes. The basic technique is a simple matrix perturbation argument combined with the Ball-Narcowich-Ward stability results. © Springer-Verlag 2004.

In this paper a local type method is proposed to smooth noisy data. Criteria of convergence and error bounds are given. An applciation is also presented for a biomedical problem in ℝ3, which is usually solved only in ℝ2. © 1984 Springer-Verlag.