Numerical Method20805 marksNumerical: Newton's backward difference interpolationNewton's Interpolation using divided differences, forward di
Newton's Backward Difference Table Construct Newton's backward difference table for given data points and approximate the value of f(x) at x=45.
Newton's Backward Difference Table
Construct Newton's backward difference table for given data points and approximate the value of $f(x)$ at $x=45$.
$$\begin{array}{c|ccccc} x & 10 & 20 & 30 & 40 & 50 \ \hline f(x) & 0.985 & 0.934 & 0.866 & 0.766 & 0.643 \end{array}$$
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x 10 20 30 40 50 ------------------------ f(x) 0.985 0.934 0.866 0.766 0.643 - Step size: $h = 10$ - $xn = 50$, $f(xn) = 0.643$ - Interpolation point: $x = 45$ - $s = \dfrac{x - xn}{h} = \dfrac{45 - 50}{10} = -0.5$ $\nabla f = f(xi) - f(x{i-1})$ First differences: - $0.934 - 0.985 = -0.051$ -