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Integration in reproducing kernel Hilbert spaces of Gaussian kernels [PDF]
Mathematics of Computation, 2021 The Gaussian kernel plays a central role in machine learning, uncertainty quantification and scattered data approximation, but has received relatively little attention from a numerical analysis standpoint. The basic problem of finding an algorithm for efficient numerical integration of functions reproduced by Gaussian kernels has ...
Toni Karvonen +2 more
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Optimal Control Problems: Convergence and Error Analysis in Reproducing Kernel Hilbert Spaces [PDF]
Control and Optimization in Applied Mathematics, 2021 In this article, we offer an efficient method to find an approximate solution for quadratic optimal control problems. The approximate solution is offered in a finite series form in reproducing kernel space.
Ebrahim Amini
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A Primer on Reproducing Kernel Hilbert Spaces [PDF]
Foundations and Trends® in Signal Processing, 2015 Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material,greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and explaining when and why these spaces are efficacious.
Jonathan H. Manton +1 more
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Metamorphosis of images in reproducing kernel Hilbert spaces [PDF]
Advances in Computational Mathematics, 2015 Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the practical application of metamorphosis is a numerical method based on shooting from the initial momentum, as this
Casey L. Richardson, Laurent Younes
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ON THE INCLUSION RELATION OF REPRODUCING KERNEL HILBERT SPACES [PDF]
Analysis and Applications, 2013 To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established.
Haizhang Zhang, Liang Zhao
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Fractal and Fractional, 2020 In this research, obtaining of approximate solution for fractional-order Burgers’ equation will be presented in reproducing kernel Hilbert space (RKHS). Some special reproducing kernel spaces are identified according to inner products and norms.
Onur Saldır +2 more
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A Generalized Norm on Reproducing Kernel Hilbert Spaces and Its Applications
Axioms, 2023 The aim of this article was to provide improved estimates for the (α,β)-norm of a bounded linear operator. In particular, our results enabled the determination of new upper bounds involving both the Berezin number and the Berezin norm of bounded linear ...
Najla Altwaijry +2 more
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Beurling-Type Theorem for a Class of Reproducing Kernel Hilbert Spaces
Journal of Mathematics, 2022 In this paper, it is proved that the Beurling-type theorem holds for the shift operator on a class of reproducing analytic Hilbert spaces.
Zhi-jie Wang +2 more
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Radial kernels and their reproducing kernel Hilbert spaces
Journal of Complexity, 2010 Let \(R\) be a continuous convex function on a Hilbert space \(H\). In learning theory, \[ A(\lambda):= \inf_{h\in H} \{\lambda\| h\|^2+ R(h)\}- \inf_{h\in H} R(h) \] is called an approximation error function. Here, \(H\) is a reproducing kernel Hilbert space (RKHS) of functions on \(\mathbb{R}^d\), i.e., such that the evaluations \(\delta_x: h\mapsto ...
Clint Scovel +3 more
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Advances in Difference Equations, 2021 This paper deals with the generalized Bagley–Torvik equation based on the concept of the Caputo–Fabrizio fractional derivative using a modified reproducing kernel Hilbert space treatment.
Shatha Hasan +5 more
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