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Performance of B spline package's "spcol" near the boundary

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Evan Scope Crafts
Evan Scope Crafts 2020-11-21
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?

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