کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4632442 | 1340645 | 2011 | 4 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Some issues on interpolation matrices of locally scaled radial basis functions Some issues on interpolation matrices of locally scaled radial basis functions](/preview/png/4632442.png)
Radial basis function interpolation on a set of scattered data is constructed from the corresponding translates of a basis function, which is conditionally positive definite of order m ⩾ 0, with the possible addition of a polynomial term. In many applications, the translates of a basis function are scaled differently, in order to match the local features of the data such as the flat region and the data density. Then, a fundamental question is the non-singularity of the perturbed interpolation (N × N) matrix. In this paper, we provide some counter examples of the matrices which become singular for N ⩾ 3, although the matrix is always non-singular when N = 2. One interesting feature is that a perturbed matrix can be singular with rather small perturbation of the scaling parameter.
Journal: Applied Mathematics and Computation - Volume 217, Issue 10, 15 January 2011, Pages 5011–5014