Quadratic splines smoothing the first derivatives
The author studies the problem of computing the quadratic spline with knots at \(a=x_ 0<x_ 1<\dots < x_ n<x_{n+1}=b\) which minimizes the expression \(\alpha\int^ b_ a[f''(x)]^ 2dx+\sum^{n+1}_{i=0}w_ i[f'(x_ i)-m_ i]^ 2\) for given values \(\{m_ i\}_ 0^{n+1}\), parameter \(\alpha\) and weights \(w_ i\geq 0\), \(i=0,\dots,n+1\).
scientific article; zbMATH DE number 64090