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Reproducing Kernel Method with Global Derivative
Journal of Function Spaces, 2023 Ordinary differential equations describe several phenomena in different fields of engineering and physics. Our aim is to use the reproducing kernel Hilbert space method (RKHSM) to find a solution to some ordinary differential equations (ODEs) that are described by using the global derivative.
Nourhane Attia +2 more
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Statistical properties of the method of regularization with periodic Gaussian reproducing kernel [PDF]
, 2004 The method of regularization with the Gaussian reproducing kernel is popular in the machine learning literature and successful in many practical applications. In this paper we consider the periodic version of the Gaussian kernel regularization.
Yi Lin, Lawrence D. Brown
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Interpolation-based reproducing kernel particle method
Computer Methods in Applied Mechanics and EngineeringMeshfree methods, including the reproducing kernel particle method (RKPM), have been widely used within the computational mechanics community to model physical phenomena in materials undergoing large deformations or extreme topology changes. RKPM shape functions and their derivatives cannot be accurately integrated with the Gauss-quadrature methods ...
Jennifer E. Fromm +2 more
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Reproducing Kernel Method for Fractional Riccati Differential Equations [PDF]
Abstract and Applied Analysis, 2014 This paper is devoted to a new numerical method for fractional Riccati differential equations. The method combines the reproducing kernel method and the quasilinearization technique. Its main advantage is that it can produce good approximations in a larger interval, rather than a local vicinity of the initial position.
Li, X. Y., Wu, B. Y., Wang, R. T.
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Reproducing Kernel Method for Solving Nonlinear Differential‐Difference Equations [PDF]
Abstract and Applied Analysis, 2012 On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential‐difference equations (NDDEs) is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution un,m is constructed by truncating the series to m terms.
Reza Mokhtari +2 more
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Solutions of nonlinear systems by reproducing kernel method
The Journal of Nonlinear Sciences and Applications, 2017 Summary: A novel approximate solution is obtained for viscoelastic fluid model by reproducing kernel method (RKM). The resulting equation for viscoelastic fluid with magneto-hydrodynamic flow is transformed to the nonlinear system by introducing the dimensionless variables.
Ali Akgül +4 more
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Path Integrals on Euclidean Space Forms [PDF]
, 2015 In this paper we develop a quantization method for flat compact manifolds based on path integrals. In this method the Hilbert space of holomorphic functions in the complexification of the manifold is used. This space is a reproducing kernel Hilbert space.
Capobianco, Guillermo, Reartes, Walter
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Kernel center adaptation in the reproducing kernel Hilbert space embedding method
International Journal of Adaptive Control and Signal Processing, 2022 SummaryThe performance of adaptive estimators that employ embedding in reproducing kernel Hilbert spaces (RKHS) depends on the choice of the location of basis kernel centers. Parameter convergence and error approximation rates depend on where and how the kernel centers are distributed in the state‐space.
Sai Tej Paruchuri +2 more
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Noncanonical Quantization of Gravity. I. Foundations of Affine Quantum Gravity [PDF]
, 1999 The nature of the classical canonical phase-space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations. Prior to the introduction of constraints, a
DeWitt B. S. +3 more
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Convergence rates of Kernel Conjugate Gradient for random design regression [PDF]
, 2016 We prove statistical rates of convergence for kernel-based least squares regression from i.i.d. data using a conjugate gradient algorithm, where regularization against overfitting is obtained by early stopping.
Blanchard, Gilles, Krämer, Nicole
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