Orthogonal splines based on B-splines — with applications to least squares, smoothing and regularisation problems
Part I Development of Algorithms 1. Spline Approximation and Applications
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Abstract
Orthogonal linear and cubic splines are introduced, based on a simple recurrence procedure using B-splines. Stable formulae are obtained for explicit least squares approximation. An application to the smoothing of noisy data is given, in which the approximation is essentially a second integral of an orthogonal linear spline and this leads to an efficient solution procedure. An application to the regularisation of integral transforms, and specifically to the finite moment problem, is also described.
Keywords
Solution Procedure Efficient Solution Noisy Data Moment Problem Regularisation Problem
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References
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© J.C. Baltzer AG, Science Publishers 1993