کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4607795 | 1337884 | 2009 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
A Newton basis for Kernel spaces
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
It is well known that representations of kernel-based approximants in terms of the standard basis of translated kernels are notoriously unstable. To come up with a more useful basis, we adopt the strategy known from Newton’s interpolation formula, using generalized divided differences and a recursively computable set of basis functions vanishing at increasingly many data points. The resulting basis turns out to be orthogonal in the Hilbert space in which the kernel is reproducing, and under certain assumptions it is complete and allows convergent expansions of functions into series of interpolants. Some numerical examples show that the Newton basis is much more stable than the standard basis of kernel translates.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 161, Issue 2, December 2009, Pages 645–655
Journal: Journal of Approximation Theory - Volume 161, Issue 2, December 2009, Pages 645–655
نویسندگان
Stefan Müller, Robert Schaback,