e will be repeatedly
calculating matrixes of the
form
for some fixed functions
and
and a scalar product
in
.
We use properties of scale and transport operations to reduce the number
scalar product evaluations.
Let
.
We
calculate
and use the formula (
Property of
scale and transport
2
).
We use the formula (
Property of
scale and transport
3
).
We use the formula (
Property of
scale and transport
7
).
Therefore, we regard the scalar product
as a function of two parameters
and
.
Together with the
rule
this significantly reduces the amount of calculation.
In case of a wavelet basis, adapted to an interval
,
we can apply this rule to the internal
functions.
