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Fasshauer, G.E. and Ye, Q. (2012) A Kernel-Based Collocation Method for Elliptic Partial Differential Equations with Random Coefficients. In: Dick, J., Kuo, F., Peters, G. and Sloan, I., Eds., Monte Carlo and Quasi-Monte Carlo Methods 2012, Springer, Berlin, 331-347.
https://doi.org/10.1007/978-3-642-41095-6_14

has been cited by the following article:

• TITLE: Solving Neumann Boundary Problem with Kernel-Regularized Learning Approach

  AUTHORS: Xuexue Ran, Baohuai Sheng

  KEYWORDS: Neumann Boundary Value, Kernel-Regularized Approach, Reproducing Kernel Hilbert Space, The Unit Ball, The Unit Sphere

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.12 No.4, April 19, 2024

  ABSTRACT: We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.