To solve the complicated interpolation problem for trivariate scattered data, a trivariate polynomial natural spline interpolation method is proposed. In the case of minimizing the objective functional with natural boundary conditions, the solution of the interpolation problem is constructed by the spline function methods of Hilbert space and in every block is a trivariate odd degree polynomial. Its expression is so simple and the coefficients can be decided by a linear system whose coefficient matrix is symmetry.
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