Abstract
This paper examines the inherent connection between the generalized Hamiltonian system and the spline function. By considering the generalized canonical multipoint boundary value (GCMBV) problem, a multipoint complementary variational principle for generalized Hamiltonian system is provided, and the sufficient and necessary condition for solvability of the GCMBV problem is obtained. With the aid of Hamiltonian equations, a new class of vector spline functions with good variational and approximation properties called H-spline are defined, it includes the general vector spline as a special one. Finally, the H-spline interpolation problems are also discussed.
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