he next step is to
implement the cascade algorithm (see the section
(
Recovering
scaling function from auxiliary function
)). The cascade algorithm starts
from a finite support
function
and then
proceeds
The function
may be chosen as
However, the procedure
is such that if
is piecewise constant then
is piecewise constant. Other piecewise polynomial expressions are acceptable
as long as the support remains finite
and
For this reason we explore several possibilities for
to a be a spline function (see the section
(
Spline functions
)) of increasing
complexity.
The absolutely minimal degree of smoothness is
.
Such requirement will be evident when we consider applications to finite
element technique.
The cascade procedure is implemented in the function "cascade" of the class
"FourFunctions" in the file "OTSProjects\python\wavelet\cascade.py".
