e start from a set
and a function
:
for a given vector
and
and
We introduce the notation
for the set of scales in the definition of
,
the
notation
for the set of translations, the notation
for the intervals of integration and the
notation
for multi-indexes.
We fix
and concentrate on calculating
where
1.
Form
2. Let
be a one-to-one onto mapping:
for some
.
For every
we form the
subdomain
and the set
of vertices of
.
For each pair
we calculate
Let
be a one-to-one onto
mapping:
for some
,
where
Let
be a one-to-one onto
mapping:
for some
,
where
Thus
indexes boundary subdomains and
indexes internal subdomains.
3. We
introduce
4. For every
we
form
and
calculate
5. For every
we
form
and calculate
as
follows:
where we adopt the
convention
and calculate
recursively in
as follows.
For
,
For
,
,
,
where
For
,
,
,
For
,
,
,
For
,
,
,
where
For
,
,
,
For
,
,
,
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