کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4640216 1341266 2011 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Bases for kernel-based spaces
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
Bases for kernel-based spaces
چکیده انگلیسی

Since it is well-known (De Marchi and Schaback (2001) [4]) that standard bases of kernel translates are badly conditioned while the interpolation itself is not unstable in function space, this paper surveys the choices of other bases. All data-dependent bases turn out to be defined via a factorization of the kernel matrix defined by these data, and a discussion of various matrix factorizations (e.g. Cholesky, QR, SVD) provides a variety of different bases with different properties. Special attention is given to duality, stability, orthogonality, adaptivity, and computational efficiency. The “Newton” basis arising from a pivoted Cholesky factorization turns out to be stable and computationally cheap while being orthonormal in the “native” Hilbert space of the kernel. Efficient adaptive algorithms for calculating the Newton basis along the lines of orthogonal matching pursuit conclude the paper.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 4, 15 September 2011, Pages 575–588
نویسندگان
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