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On algorithms for parabolic splines. (English) Zbl 0693.65005

Let \(a=x_ 0<x_ 1<...<x_{n+1}=b\) be a partition of the interval [a,b]. The following problem is discussed. Given a set of real numbers \(\{g_ i:\) \(0\leq i\leq n\}\). Find a quadratic spline \(S_ 2\in C^ 1[a,b]\), with knots at \(x_ 0,x_ 1,...,x_{n+1}\), such that \((1)\quad S_ 2(t_ i)=g_ i\quad (0\leq i\leq n).\) The nodes \(t_ i\) (0\(\leq i\leq n)\) are such that \(t_{i-1}<x_ i<t_ i\quad (1\leq i\leq n);\quad t_ 0=a,\quad t_ n=b.\) Imposing two extra boundary conditions the author shows that there exists a unique spline \(S_ 2\) which satisfies the interpolatory conditions (1). An algorithm for numerical evaluation of the quadratic spline interpolant \(S_ 2\) is included.
Reviewer: E.Neuman

MSC:

65D07 Numerical computation using splines
41A15 Spline approximation
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References:

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