A fast dual iterative algorithm for convexly constrained spline smoothing

This paper proposes fast iterative algorithms for solving convexly constrained spline smoothing through a characterization of solutions in a primal-dual space. In view of achievements for fast implementations of spline interpolation, the update of the proposed algorithm is designed as the composition of solving a spline interpolation problem and computing the projection onto the constraint set. In addition, the update of the proposed algorithm is performed in an efficient dimensional space having the same size as given observations. These desired properties significantly reduce the computational cost in the update, which is demonstrated by a numerical example.

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