(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**