| Abstract: | Based on the general Hilbert space theory of spline interpolation, multivariate natural polynomial spline functions are introduced as a generalization of the well-known univariate natural polynomial splines. Explicit formulations of these spline interpolants without boundary conditions to scattered data on certain bounded domains in R^s are constructed. It turns out that these new multivariate spline interpolants are fairly easy to implement and hence should be very useful in multivariate numerical analysis, such as numerical integrations and numerical solutions of partial differential equations. |
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