Correction to: Jumping with variably scaled discontinuous kernels (VSDKs)
نویسندگان
چکیده
منابع مشابه
Interpolation with Variably Scaled Kernels
Within kernel–based interpolation and its many applications, it is a well–documented but unsolved problem to handle the scaling or the shape parameter. We consider native spaces whose kernels allow us to change the kernel scale of a d–variate interpolation problem locally, depending on the requirements of the application. The trick is to define a scale function c on the domain Ω ⊂ Rd to transfo...
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In kernel–based methods, how to handle the scaling or the choice of the shape parameter is a well– documented but still an open problem. The shape or scale parameter can be tuned by the user according to the applications, and it plays a crucial role both for the accuracy of the method and its stability. In [7], the Variably Scaled Kernels (VSKs) were introduced. The idea is to vary the scale in...
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David Vogan has pointed out that Lemma 5.3 is incorrect, even for matrix groups, and therefore some changes are needed in the statements of the main theorems. The changes in question are not decisive, but we feel that the accurately stated versions of the theorems should be in the literature. Actually, when changes are needed, the new results yield more Szegi5 mappings than were originally pred...
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whose kernel k(t, s) is either discontinuous or not smooth along the main diagonal, is presented. This scheme is of spectral accuracy when k(t, s) is infinitely differentiable away from the diagonal t = s, and is also applicable when k(t, s) is singular along the boundary, and at isolated points on the main diagonal. The corresponding composite rule is described. Application to integro-differen...
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ژورنال
عنوان ژورنال: BIT Numerical Mathematics
سال: 2020
ISSN: 0006-3835,1572-9125
DOI: 10.1007/s10543-020-00800-9