Some results on Tchebycheffian spline functions |
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Authors: | George Kimeldorf |
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Institution: | Department of Statistics, Florida State University, Tallahassee, Florida 32306 USA; Department of Statistics, University of Wisconsin, Madison, Wisconsin 53706 USA |
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Abstract: | This report derives explicit solutions to problems involving Tchebycheffian spline functions. We use a reproducing kernel Hilbert space which depends on the smoothness criterion, but not on the form of the data, to solve explicitly Hermite-Birkhoff interpolation and smoothing problems. Sard's best approximation to linear functionals and smoothing with respect to linear inequality constraints are also discussed. Some of the results are used to show that spline interpolation and smoothing is equivalent to prediction and filtering on realizations of certain stochastic processes. |
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