Performance of B spline package's "spcol" near the boundary
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I am working on a project where I am attempting to fit data that lies at evenly spaced locations, i.e.
, using cubic B-splines. To do this, I am using the built in Matlab function "optknt" to create the knot vector, and then examining the resulting matrix A formed by "spcol". The knot vector generated by "optknt" has four knots at
, and four knots at
. Examining the Cox-De-Boor recurison relationship as defined, e.g. here - https://en.wikipedia.org/wiki/De_Boor%27s_algorithm, it seems as if the B-splines
will be uniformly 0, as $N$ does not satisfy
for any i, where t is the knot vector. Thus, it seems that the last row of A should be a zero vector. However,
when A is computed using "spcol". Why is this?
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/422378/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/422383/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/422388/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/422393/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/422398/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/422403/image.png)
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