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If each spline is given in the form of

g_{i}(x) = a_{i}(x-x_{i})^{3}+ b_{i}(x-x_{i})^{2}+ c_{i}(x-x_{i}) + d_{i}

where i = 1 to N for N+1 data points.

Then given that b_{1}and b_{N+1}are zero (because the second derivatives are zero at the endpoints, due to this being a natural cubic spline), then there are N-1 equations for b_{2}....b_{N}.

Since we then use the value of b_{i}to work out the unknowns a_{i}, c_{i}and d_{i}then there are four equations per i. Then since b_{i}and b_{N+1}are zero, we can work out a_{i}, c_{i}and d_{i}on the last splines (3 each).

So is the answer 4(N-1) +6?

I don't understand what it means by 'Show there are enough equations..', any ideas?

Thanks

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# Homework Help: I don't fully understand this question about cubic spline interpolation

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