Introduction
A univariate piecewise
polynomial
is specified by its break sequence breaks and
the coefficient array coefs of
the local power form (see Equation 4-1 below) of its polynomial pieces; see Tensor Product Splines for a discussion
of multivariate piecewise-polynomials. The coefficients may be (column-)vectors,
matrices, even ND-arrays. For simplicity, the present discussion deals
only with the case when the coefficients are scalars.
The break sequence is assumed to be strictly increasing,
breaks(1)
< breaks(2) < ... < breaks(l+1)
with l the number of polynomial pieces that
make up
.
While these polynomials may be of varying degrees, they are
all recorded as polynomials of the same order k,
i.e., the coefficient array coefs is of size [l,k],
with coefs(j,:) containing the k coefficients
in the local power form for the jth
polynomial piece, from the highest to the lowest power; see Equation 4-1 below.
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