Constructing a natural cubic spline
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Please baby step me through the solution. For example, how the heck did they get b0 = 3/4? It should bereally simple (seems like it's just a bunch of substitutions for known values), but for some reason I have no idea how to find it.
I get that a0 = 2, a1 = 3, and c0 = 0. So now c1 = 2*d0. But there's nothing that isolates d0, so we can't easily find c1. Alternatively, we can see that 3 = 2 + b0 + d0, but no matter how many times i isolate b0, i can't seem to find a value for it either.
Thank you in advance.
Resized the picture.. Sorry about that.
Well, you need to solve the linear system of the 5 remaining variables since a0=2, a1=3, c0=0 are already given.
This leads to
b0 + d0 = 3 - a0 = 3- 2 = 1
b1 + c1 + d1 = 5 - a1 = 2
b0 + 3d0 = b1
6d0 = 2c1 => c1 = 3d0
2c1 + 6d1 = 0 => c1 = -3d1 => d1 = -d0
Now we can insert b1,c1,d1 in the second equation:
(b0 + 3d0) + (3d0) + (-d0) = 2
b0 + 5d0 = 2
b0 + d0 = 1 => 4d0 = 1, d0 = 1/4, b0 = 3/4 and so on.
