Abstract
The problem of determining polynomial spline approximations subject to derivative boundary conditions is considered. It is shown that if B-splines are employed as a basis, the incorporation of a variety of boundary conditions and the solution of the resulting equations for the B-spline coefficients can be carried out in an efficient and stable manner. The methods discussed can be applied to interpolating splines and to splines which approximate discrete data sets in the least squares sense. The boundary conditions can normally be incorporated by extending and refining existing algorithms rather than by designing entirely new ones.
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Cox, M.G. (1978). The incorporation of boundary conditions in spline approximation problems. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067696
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DOI: https://doi.org/10.1007/BFb0067696
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