Multi-wavelets from spline super-functions with approximation order

Approximation order is an important feature for all wavelets. It implies that polynomials up to degree p-1 are in the space spanned by the scaling function(s). For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix H_f, a finite portion of H, determine the combinations of scaling functions that produce the desired spline or scaling function. In this work, the condition of approximation order is derived for the special case where the multi scaling functions combine to form a super function that can produce any desired polynomial. New multi-wavelets with approximation orders one and two are constructed