Newton's Interpolation What is Newton's interpolation? Obtain the divi | Numerical Method 2078

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Numerical Method20785 marksNumerical: Newton's divided difference interpolationNewton's Interpolation using divided differences, forward di

Newton's Interpolation

What is Newton's interpolation? Obtain the divided difference table from the following data set and estimate the f(x) at x = 2 and x = 5.

$\begin{array}{c|ccccc} x & 3.2 & 2.7 & 1.0 & 4.8 & 5.6 \\ \hline f(x) & 22.0 & 17.8 & 14.2 & 38.3 & 51.7 \end{array}$

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Newton's Interpolation

What is Newton's interpolation? Obtain the divided difference table from the following data set and estimate the f(x) at x = 2 and x = 5.

$$\begin{array}{c|ccccc} x & 3.2 & 2.7 & 1.0 & 4.8 & 5.6 \ \hline f(x) & 22.0 & 17.8 & 14.2 & 38.3 & 51.7 \end{array}$$

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Newton's interpolation constructs an interpolating polynomial through unequally (or equally) spaced data points using divided differences. Its form is: $Pn(x) = f[x0] + f[x0,x1](x-x0) + f[x0,x1,x2](x-x0)(x-x1) + \cdots$ $i$ $xi$ $f(xi)$ ---------------------- 0 3.2 22.0 1 2.7 17.8 2 1.0 14.2 3 ...

Newton's interpolation constructs an interpolating polynomial through unequally (or equally) spaced data points using divided differences. Its form is: $$Pn(x) = f[x0] + fx0,x1 + fx0,x1,x2(x-x1) + \cdots$$ $i$ $xi$ $f(xi)$ ---------------------- 0 3.2 22.0 1 2.7 17.8 2 1.0 14.2 3 ...

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