Consider the following data: egin{tabular}{c|c} ( x ) & ( f(x) ) \ hline 0.8 & 0.22363362 \ 1.0 & 0.65809197 end{tabular} 1. Construct the clamped cubic spline using the fact that ( f^{prime}(0.8)=2.1691753 ) and ( f^{prime}(1.0)= ) 2.0466965 . 2. Use the cubic spline constructed in part (1) to approximate ( f(0.9) ) and ( f^{prime}(0.9) ) for the function ( f(x)=sin left(e^{x}-2 ight) ). Calculate the actual error.
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Step 1
In this case, we have one interval between x = 0.8 and x = 1.0. Step 2: Determine the coefficients for the clamped cubic spline. Since we have one interval, we need to determine the coefficients for one cubic polynomial. Step 3: Set up the system of Show more…
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