e continue derivations of the previous section
(
Calculation of
boundary scaling functions
). We modify the procedure of the section
(
Adapting dual
wavelets to interval [0,1]
) to improve numerical stability.
In light of the remark (
Dimension mismatch
),
some of the
may have nearly zero
norm.
We discard such functions and obtain the basis to match the
requirement
Afterwards, we
normalize
the obtained functions.
The procedure is implemented in the script "bases\psi.py" and tested by the
script "_run_bases.py". The flat version (no classes) of the procedure may be
found in the file tApprox.py. The same file performs various tests. In
particular, we verify directly that we have the scaling relationship and low
condition numbers for various Gram matrixes.
