(Solved): run matlab and show matlab file7c. onlyalgorithm 3.5 7. Construct the clamped cubic spline using the ...

7. Construct the clamped cubic spline using the data of Exercise 3 and the fact that a. $f^{?}(8.3)=1.116256$ and $f^{?}(8.6)=1.151762$. b. $f^{?}(0.8)=2.1691753$ and $f^{?}(1.0)=2.0466965$. c. $f^{?}(?0.5)=0.7510000$ and $f^{?}(0)=4.0020000$. d. $f^{?}(0.1)=3.58502082$ and $f^{?}(0.4)=2.16529366$. c. To construct the cubic spline interpolant $S$ for the function $f$ defined at the numbers $x_0<x_1<?<x_n$, satisfying $S^{?}\left(x_0\right)=f^{?}\left(x_0\right)$ and $S^{?}\left(x_n\right)=f^{?}\left(x_n\right)$ : INPUT $n;x_0,x_1,\dots ,x_n;a_0=f\left(x_0\right),a_1=f\left(x_1\right),\dots ,a_n=f\left(x_n\right);FPO=f^{?}\left(x_0\right);$ $FPN=f^{?}\left(x_n\right)$. OUTPUT $a_j,b_j,c_j,d_j$ for $j=0,1,\dots ,n?1$. (Note: $S(x)=S_j(x)=a_j+b_j\left(x?x_j\right)+c_j{\left(x?x_j\right)}^2+d_j{\left(x?x_j\right)}^3$ for $x_j?x?x_{j+1}$.) Step 1 For $i=0,1,\dots ,n?1$ set $h_i=x_{i+1}?x_i$. Step 2 Set ${?}_0=3\left(a_1?a_0\right)/h_0?3FPO$; ${?}_n=3FPN?3\left(a_n?a_{n?1}\right)/h_{n?1}\text{. }$ Step 3 For $i=1,2,\dots ,n?1$ $\mathrm{set}{?}_i=\frac{3}{h_i}\left(a_{i+1}?a_i\right)?\frac{3}{h_{i?1}}\left(a_i?a_{i?1}\right).$ Step 4 Set $l_0=2h_0:$ (Steps 4, 5, and 6 and part of Step 7 solve a tridiagonal linear system using a method described in Algorithm 6.7.) $\begin{array}{l}{?}_0=0.5;\\ z_0={?}_0/l_0.\end{array}$ Step 5 For $i=1,2,\dots ,n?1$ $\begin{array}{rl}\mathrm{set}& l_i=2\left(x_{i+1}?x_{i?1}\right)?h_{i?1}{?}_{i?1};\\ {?}_i& =h_i/l_i\\ z_i& =\left({?}_i?h_{i?1z_{i?1}}\right)/l_i.\end{array}$