Compact Matérn Kernels and Piecewise Polynomial Splines Viewed From a Hilbert-Schmidt Perspective
نویسندگان
چکیده
Differential operators and associated boundary conditions have been used to define interpolating splines, such as L-splines, since the mid 1960s. This work adapts that approach to define kernels which can be used to perform equivalent interpolation. While a closed form of these kernels is generally unavailable, their eigenexpansions can be determined by solving the Sturm-Liouville eigenvalue problem arising from the given differential operator and boundary conditions, allowing for computation with the kernels using the RBF-QR technique. Numerical results involving these methods show convergence orders commensurate with L-spline theory.
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