he script in the file
"_run_cascade.py" explores convergence of the scaling procedure for a variety
of
.
We are trying to achieve acceptable precision of the final result
or
for one of the functions for a minimal number of steps of the scaling
procedure. Minimization of the number of steps is important because every
steps doubles the number of intervals in the piecewise polynomial description
of the result.
For
(the number of vanishing moments), numerical experimentation shows that
and
are optimal choices. The lower splines suffer from poor approximation. The
higher splines struggle with numerical stability. The
-difference
between successive steps of the scaling procedure halves at every step. One of
the scaling functions has the precision
after 5 steps in case of
and precisions
after 4 and 5 steps in case of
.
The choice
carries additional advantage of continuity of first derivative. For this
reason we concentrate on such choice.
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