Given a pair of biorthogonal multiscaling
functions, we present an algorithm for raising
their approximation orders to any desired level.
Precisely, let
and be a pair of biorthogonal multiscaling functions
of multiplicity
r, with approximation orders
m and , respectively. Then for some integer
s, we can construct a pair of new biorthogonal
multiscaling functions
and
with approximation orders
n
() and
(), respectively. In addition, corresponding to
and , a biorthogonal multiwavelet pair
and
is constructed explicitly. Finally, an example
is given.
