write in matlabThe algorithm for the divided difference formulas for the Hermite polynomial

coefficients is:

INPUT $x=(x_0,$dots,$x_n),Y=(f(x_0),$dots,$f(x_n)),YP=(f^{\text{'}}(x_0),$dots,$f^{\text{'}}(x_n))$

OUTPUT $Q_{i,j},$ the appropriate divided differences, where the Hermite interpolating

polynomial is $H_{2n+1}(x)=Q_{0,0}+{\displaystyle \underset{i=1}{\overset{2n+1}{}}}{Q}_{i,i}pro{d}_j=0^{i-1}(z-z_j)$ and $z_{2i}=x_i,z_{2i+1}=x_i$ for $i=0,$dots,$n$

STEP $1.$ For $i=0,1,$dotsn

$z_{2i}=x_i$

$z_{2i+1}=x_i$

$Q_{2i,0}=f(x_i)$

$Q_{2i+1,0}=f(x_i)$

$Q_{2i+1,1}=f^{\text{'}}(x_i)$

$Ifi0$ then

$Q_{2i,1}=\frac{Q_{2i,0}-Q_{2i-1,0}}{z_{2i}-z_{2i-1}}$

End If

End

STEP $2.$ For $i=2,3,$dots,$2n+1$

For $j=2,3,$dots,$i$

$Q_{{?}_{?}}(i,j)=\frac{Q_{i,j-1}-Q_{i-1,j-1}}{z_i-z_{i-j}}$

End

End

STEP $3.$ OUTPUT $Q_{i,j}$