Cardinal B-spline dictionaries on a compact interval

The prescription for constructing dictionaries for cardinal spline spaces on a compact interval is given in [3]. It is proved there that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of cardinal B-spline functions of broader support that the corresponding basis function. In other words, cardinal B-spline dictionaries provide an alternative way of increasing the dimension of the space. If one were to use a basis for representing a spline space the way of increasing the space dimension would be to decrease the distance, $b$, between knots. However, through B-spline dictionaries one can increase the dimension by maintaining the same distance between knots and including functions arising by simple translations of the basis function into the knots (with distance $b'$ for $b/b'=$integer) of the space that one wishes to span.

The main code for constructing B-spline dictionaries on a compact interval is the routine TESTSPLINE.M. Inside of this routine you can set up the interval to consider, number $L$ of discretizing points, parameters $b$ (it is $b1$ in the file) and $b'$ (it is $b2$ in the file), order $m\geq1$ of splines and the type of the dictionary, either ESEP or EPKB.