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Numerical methods for solving Schrödinger equations in complex reproducing kernel Hilbert spaces
Mathematical Sciences, 2020In this paper, complex reproducing kernel Hilbert spaces and their reproducing kernels are introduced. The reproducing kernel is constructed by combining Gaussian radical basis function kernel and spline kernel. In the spaces, using the related theory, a novel numerical method is developed to solve Schroinger equations. The present method is a meshless
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Regression models for functional data by reproducing kernel Hilbert spaces methods
Journal of Statistical Planning and Inference, 2007Abstract Non-parametric regression models are developed when the predictor is a function-valued random variable X = { X t } t ∈ T . Based on a representation of the regression function f ( X ) in a reproducing kernel Hilbert space such models generalize the classical setting used in statistical learning theory.
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2011 International Conference on Communications, Computing and Control Applications (CCCA), 2011
This paper proposes a new method for online identification of a nonlinear system modelled on Reproducing Kernel Hilbert Space (RKHS). The proposed SVD-KPCA method uses the SVD technique to update the principal components. Then we use the Reduced Kernel Principal Component Analysis (RKPCA) to approach the principal components which represent the ...
Hassani Messaoud +2 more
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This paper proposes a new method for online identification of a nonlinear system modelled on Reproducing Kernel Hilbert Space (RKHS). The proposed SVD-KPCA method uses the SVD technique to update the principal components. Then we use the Reduced Kernel Principal Component Analysis (RKPCA) to approach the principal components which represent the ...
Hassani Messaoud +2 more
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Journal of Optimization Theory and Applications, 2012
In this article, we implement a relatively new analytical technique, the reproducing kernel Hilbert space method (RKHSM), for solving integro-differential equations of fractional order. The solution obtained by using the method takes the form of a convergent series with easily computable components. Two numerical examples are studied to demonstrate the
Shaher Momani, Yong Zhou, Samia Bushnaq
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In this article, we implement a relatively new analytical technique, the reproducing kernel Hilbert space method (RKHSM), for solving integro-differential equations of fractional order. The solution obtained by using the method takes the form of a convergent series with easily computable components. Two numerical examples are studied to demonstrate the
Shaher Momani, Yong Zhou, Samia Bushnaq
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Solving Fredholm integro–differential equations using reproducing kernel Hilbert space method
Applied Mathematics and Computation, 2013In this study, the numerical solution of Fredholm integro-differential equation is discussed in a reproducing kernel Hilbert space. A reproducing kernel Hilbert space is constructed, in which the initial condition of the problem is satisfied. The exact solution ux is represented in the form of series in the space W"2^2[a,b].
Nabil Shawagfeh +2 more
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Speech enhancement method based on low-rank approximation in a reproducing kernel Hilbert space
Applied Acoustics, 2016Abstract Speech signal is corrupted unavoidably by noisy environment in subway, factory, and restaurant or speech from other speakers in speech communication. Speech enhancement methods have been widely studied to minimize noise influence in different linear transform domain, such as discrete Fourier transform domain, Karhunen-Loeve transform domain ...
Yanping Zhao +3 more
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Solutions of Nonlinear System of Differential Equations by Reproducing Kernel Hilbert Space Method
Journal of Advanced Physics, 2018In this paper, we use the reproducing kernel Hilbert space method to nonlinear differential systems of equations. We verify the applicability and efficiency of the method by some examples. We showed our results by figures. Obtained Results prove that the reproducing kernel Hilbert space method is very impressive method.
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Responsive materials architected in space and time
Nature Reviews Materials, 2022Xiaoxing Xia +2 more
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