An algorithm for constructing biorthogonal multiwavelets with higher approximation orders

Given a pair of biorthogonal multiscaling functions, we present an algorithm for raising their approximation orders to any desired level. Precisely, let Φ(x) and (x) 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 Φnew(x) = [ΦT (x), φr+1 (x), φr+2(x),… φr+s(x)]T and new(x) = [ (x) T, r+1(x), r+2(x),… r+s(x)]T with approximation orders n (n > m) and ñ (ñ > ), respectively. In addition, corresponding to Φnew(x) and new(x) a biorthogonal multiwavelet pair ψnew(x) and new(x) is constructed explicitly. Finally, an example is given.