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Spline fitting with exact boundaries http://forum.alglib.net/viewtopic.php?f=2&t=4360 
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Author:  Bbllaaddee [ Sun Oct 04, 2020 11:08 pm ] 
Post subject:  Spline fitting with exact boundaries 
I'm using interpolation package to fit some data with a predefined amount of cubic splines. However, the function spline1dfit(...) uses socalled natural boundary conditions in this problem, i.e. S''=0 on boundaries. In my task I want to use this fitted region of a function with other functions on its edges. So, for example, I fit a [x1, x2] region with f1(x), [x2, x3] with splines, and [x3, x4] with f2(x). I know exactly the values and the derivatives of f1(x) and f2(x) on those points, so I wonder, if I should somehow try to implement exact boundary conditions on the fitting procedure, or may be I should switch to interpolation instead. Thanks 
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