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Reproducing Kernels and Finite Order Kernels
1991Recent literature on density and regression function estimation has shown the interest of kernels of order s, i.e. kernels with (s-1) vanishing moments. We define here a multi-stage procedure to build estimates based on increasing order kernels and leading to a data-driven choice of both the order and the smoothing parameter. Some asymptotic as well as
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Reproducing kernel particle methods
, 1995Wing Kam Liu, S. Jun, Y. Zhang
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Reproducing kernels and Riccati equations.
2001Summary: The purpose of this paper is to exhibit a connection between the Hermitian solutions of matrix Riccati equations and a class of finite-dimensional reproducing kernel Krein spaces. This connection is then exploited to obtain minimal factorizations of rational matrix-valued functions that are \(J\)-unitary on the imaginary axis in a natural way.
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An Introduction to the Theory of Reproducing Kernel Hilbert Spaces
, 2016V. Paulsen, M. Raghupathi
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Reproducing kernel Hilbert spaces
2011Hinter der Konstruktion von Hilberträumen mit reproduzierendem Kern verbirgt sich eine Theorie von Bijektionen bzw. Transformationen, die einen positiv definiten Kern mit einem Hilbertraum von Funktionen verbindet. Das Ziel dieser Diplomarbeit ist es einen Überblick über die Theorie der Hilberträume mit reproduzierendem Kern und ihrer Anwendungen zu ...
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2003
In this survey article, we would like to show that the theory of reproducing kernels is fundamental, is beautiful and is applicable widely in mathematics. At the same time, we shall present some operator versions of our fundamental theory in the general theory of reproducing kernels, as original results.
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In this survey article, we would like to show that the theory of reproducing kernels is fundamental, is beautiful and is applicable widely in mathematics. At the same time, we shall present some operator versions of our fundamental theory in the general theory of reproducing kernels, as original results.
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When and why PINNs fail to train: A neural tangent kernel perspective
Journal of Computational Physics, 2022Sifan Wang, Xinling Yu
exaly

