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Grozev, Georgi R.

Comparison theorems for L-monosplines of minimal norm. (English) Zbl 0678.41007

Numer. Math. 56, No. 4, 331-343 (1989).
Summary: Let \(LM_ N\) be the set of all L-monosplines with N free knots, prescribed by a pair (x;E) of points \(x=\{x_ i\}^ n_ 1\), \(a<x_ 1<...<x_ n<b\) and an incidence matrix \(E=(e_{ij})^ n_{i=1},^{r- 1}_{j=0}\) with \(| E| =\sum^{n}_{i=1}\sum^{r- 1}_{j=0}e_{ij}\leq N.\) Denote by \(LM^ 0_ N\) the subset of \(LM_ N\) consisting of the L-monosplines with N simple knots \((n=N)\). We prove that the L-monosplines of minimal \(L_ p\)-norms in \(LM_ N\) belong to \(LM^ 0_ N\). The results are reformulated as comparison theorems for quadrature formulae.

MSC:

41A15 Spline approximation
41A55 Approximate quadratures

Keywords:

L-monosplines; minimal \(L_ p\)-norms; quadrature formulae
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\textit{G. R. Grozev}, Numer. Math. 56, No. 4, 331--343 (1989; Zbl 0678.41007)
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References:

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