On the Problems of Smoothing and Near-Interpolation
Mathematics of Computation
In the first part of this paper we apply a saddle point theorem from convex analysis to show that various constrained minimization problems are equivalent to the problem of smoothing by spline functions. In particular, we show that near-interpolants are smoothing splines with weights that arise as Lagrange multipliers corresponding to the constraints in the problem of near-interpolation. In the second part of this paper we apply certain fixed point iterations to compute these weights. A similar iteration is applied to the computation of the smoothing parameter in the problem of smoothing.
Kersey, Scott N..
"On the Problems of Smoothing and Near-Interpolation."
Mathematics of Computation, 72 (244): 1873-1885.