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Peano kernel theorem

The Peano kernel theorem represents a linear approximation error

L

that annihilates polynomials below degree

r

as

L (f) = \int_{a}^{b} K (t) f^{(r)} (t) d t, K (t) = L (\frac{( x - t ) _{+}^{r - 1}}{( r - 1 )!}) .

Table of contents 56 2
- Four-point one-sided second-derivative formula Peano kernel theorem 36 1
  - Sharp Peano-kernel constant for the four-point endpoint second derivative Four-point one-sided second-derivative formula 27

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