Discrete polynomial spline approximation methods
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Discrete splines were introduced by Mangasarian and Schumaker  as solutions to certain minimization problems involving differences. They can be defined as piecewise polynomials where the ties between each polynomial piece involve continuity of differences instead of derivatives. We study discrete analogs of local spline approximations, least squares spline approximations, and even order spline interpolation at knots. Error bounds involving differences over a finite number of points are given in each case. These contain classical error bounds as a special case.
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