Numerical Method20755 marksNumerical: polynomial interpolationLagrange's Interpolation
Find the lowest degree polynomial, which passes through the following points. Using this polynomial estimate f(x) at x = 0.
Find the lowest degree polynomial, which passes through the following points. Using this polynomial estimate f(x) at x = 0.
$$\begin{array}{c|cccccc} X & -2 & -1 & 1 & 2 & 3 & 4 \ \hline F(x) & -19 & 0 & 2 & -3 & -4 & 5 \end{array}$$
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X -2 -1 1 2 3 4 ----------------------- F(x) -19 0 2 -3 -4 5 Find the lowest degree polynomial through these 6 points, then estimate $f(0)$. Using Newton's Divided Difference Interpolation. First differences: $$f[x0,x1]=\frac{0-(-19)}{-1-(-2)}=\frac{19}{1}=19$$ $$f[x1,x2]=\frac{2-0}{1-(-1)}=\frac...