Quadratic splines smoothing the first derivatives. (English) Zbl 0757.65006

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 \(w_ i\geq 0\), \(i=0,\dots,n+1\).


65D07 Numerical computation using splines
65D05 Numerical interpolation
65D10 Numerical smoothing, curve fitting
41A15 Spline approximation
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