## 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

### Keywords:

parabolic splines; interpolation; quadratic spline; algorithm
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### References:

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