Newton Beispiel 2

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7 Gebrochenrationale Funktionen

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7.2 Interpolationspolynome

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7.2.1 Interpolationspolynome nach Newton

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$i$	$0$	$1$	$2$

$x_{i}$	$- 1$	$1$	$2$

$y_{i}$	$0$	$2$	$4$

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$x_{i}$	$y_{i}$
$- 1$	0 c0
		$γ_{01} = \frac{2 - 0}{2} =$ 1 c1
$1$	$2$		$γ_{02} = \frac{2 - 1}{3} =$ 1 3 c3
		$γ_{12} = \frac{4 - 2}{1}$
$2$	$4$

p (x) = 0 + 1 \cdot (x + 1) + \frac{1}{3} (x + 1) (x - 1) = \frac{x^{2}}{3} + x + \frac{2}{3}

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(x_{3}, y_{3}) = (3, 5)

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$x_{i}$	$y_{i}$
$- 1$	0
		1
$1$	$2$		1 3
		$2$		$\frac{- \frac{1}{2} - \frac{1}{3}}{3 - (- 1)} = \frac{- 5}{24}$
$2$	$4$		$- \frac{1}{2}$
		$1$
$3$	$5$

\frac{1 - 2}{3 - 1} = - \frac{1}{2}

p (x) = 0 + 1 (x - (- 1)) + \frac{1}{3} (x - (- 1)) (x - 1) + - \frac{5}{24} (x - (- 1)) (x - 1) (x - 2)

p (x) = - \frac{5}{24} x^{3} - \frac{1}{12} x^{2} + \frac{29}{24} x + \frac{11}{24}

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Maple: newton.mws.mw

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