摘要
The connection between spline interplation and MPBVP is dealt with and the research has been carried out with emphasis on the latter in this paper. With the aid of adjoint MPBVP, the sufficient and necessary conditions of the resolvability of the MPBVP have been provided and the solution is expressed by means of Green’s function. In absence of uniqueness of the solution, the minimum norm generalized solution is defined, its existence and uniqueness have been confirmed, and the generalized Green’s function has been constructed. Finally, the applications of the above theory to spline interpolation are given.
The connection between spline interplation and MPBVP is dealt with and the research has been carried out with emphasis on the latter in this paper. With the aid of adjoint MPBVP, the sufficient and necessary conditions of the resolvability of the MPBVP have been provided and the solution is expressed by means of Green's function. In absence of uniqueness of the solution, the minimum norm generalized solution is defined, its existence and uniqueness have been confirmed, and the generalized Green's function has been constructed. Finally, the applications of the above theory to spline interpolation are given.
