Derivation of structural characteristics of differential operator interpolating splines by the criteria of optimal control
基于最优控制理论的微分算子插值样条构造性质的新证法

The optimal control theory is applied to investigate interpolating splines associated with arbitrary linear differential operators. The differential operator interpolating splines are considered a linear optimal control problem; the structure and the continuity property of differential operator interpolating splines are derived from the necessary conditions of the optimal control with constrained states. This method not only facilitates the derivation of the well-known structure and the continuity property of differential operator interpolating splines, but also obtains as well the jerk formula at nodes of splines after the operation of the differential operator, further revealing the relation between the differential operator interpolating splines and the optimal control and providing a new approach to the study of structural properties for obstructed operator interpolating splines.