A Newton basis for kernel spaces (Q1048982)

Observing that representations of kernel-based approximants in terms of the standard basis of translated kernels are notoriously unstable [see \textit{B. J. C. Baxter}, Comput. Math. Appl. 43, No. 3-5, 305--318 (2002; Zbl 1002.65018)], the authors construct a new type of basis by mimicking the Newton interpolation formula. The stability properties of the new basis are shown to lie right between those of the standard and the Lagrange bases. Some numerical examples in support of the theoretical results of the paper have been also given.