Curve and surface fitting with splines
Curve and surface fitting with splines
Best Near-Interpolation by Curves: Existence
SIAM Journal on Numerical Analysis
Existence of set-interpolating and energy-minimizing curves
Computer Aided Geometric Design
Constrained variational refinement
Journal of Computational and Applied Mathematics
Existence of set-interpolating and energy-minimizing curves
Computer Aided Geometric Design
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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.