Abstract. In this paper, we introduce a new technique for determining in- terpolating cubic spline functions with clamped boundary condition. By in- troducing an arti¯cial cost functional and use the important minimum-norm property of spline functions, the problem is modi¯ed into one consisting of the minimization of a positive linear functional over a set of Radon measures. Then we obtain an optimal measure which is approximated by a ¯nite com- bination of atomic measures, and by using atomic measures we change this one to a ¯nite dimensional linear programming problem. Finally we ¯nd a piecewise constant optimal control function on every subinterval and then the approximated interpolating cubic spline functions. Some examples are given show the procedure.

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