Kernel–Based Meshless Methods
نویسنده
چکیده
2 Kernels 1 2.1 Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2.2 Positive Definiteness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 General Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Inner Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Duality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.6 Native Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.7 Reproducing Kernel Hilbert Spaces . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.8 Kernels for Orthogonal Expansions . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.9 Native Spaces of Mercer Kernels . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.10 Finite Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.11 Kernels for Univariate Sobolev Spaces . . . . . . . . . . . . . . . . . . . . . . . . 20
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