Abstract :
Given points 0 = t1 < ··· < tn = 1, real numbers yi, i = 1, ..., n, and piecewise linear splines e and d with knots ti such that e(ti) < yi < d(ti) we consider the problem to find a function ƒ with minimal L2-norm of the second derivative and which satisfies the conditions ƒ(ti) = yi, i = 1, ..., n, and e(t) ≤ƒ(t)≤d(t) for all t ∈ [0,1]. We prove that the solution of this problem is a cubic spline which depends continuously on the data.
