Find the natural cubic splinc that passes through the points

Find the natural cubic splinc that passes through the points (-3,2), (-2,0), (1,3) and (4,1) with the free boundary conditions S\"(-3) = 0 and S\"(4) = 0.

Solution

Solving the system of linear equations for the spline with the given conditions,

f(x)=0.4713x³+4.2414x²+10.2529x+7.3103,if x[3,2]

=,0.2427x³+0.0421x²+1.6858x+1.599,if x[2,1]

=,0.0856x³+1.0268x²+2.6705x+1.2708,if x[1,4].