Algorithm For The Construction Of Interpolating Scaling Vectors

In this paper we investigate the orthogonal interpolating scaling vectors, which has the formwhere the scaling vectorsΦ= (φ₀,…,φ_m-1)^T belongs to (L¹(R^d))^r, {ρ_i} is the completeset of representatives of Z^d/MZ^d ,and M is d×d integer matrix. After introducingthe algorithm for construction of interpolating scaling vectors, we obtain that this kind of orthogonal interpolating scaling vectors constructed by the algorithm can not be symmetric, moreover, we obtain the necessary conditions for constructing symmetric orthogonal interpolating scaling vectors. we also obtain: letΦ= (φ₀,…,φ_r-1)^T be the normalized solution of refinement equation(1.1), and if the mask of (1.1) satisfies (2.1), thenΦis interpolating if and only if the Cascade algorithm converges.