A NEW NUMERICAL METHOD FOR INTERPOLATING CUBIC SPLINE FUNCTIONS WITH CLAMPED BOUNDARY CONDITION

In this paper, we introduce a new technique for determining interpolating cubic spline functions with clamped boundary conditon. By intriducing an artificial cost functional and use the important minimum-norm property of spline functions, the problem is modified into one consisting of the minimaization of a positine linear functional over a set of Radon measures. Then we obtain an optimal measure which is approximated by a finite combination of atomic measures, and by using atomic measures we change this one to a finite dimensional linear programming problem. Finally we find a piecewies constant optimal function on every subinterval and then the approximated interpolating cubic spline functions. Some examples are given show the procedure.

Keywords:

Interpolating cubic spline functions , optimal control , measre theory , linear programming