Matrix extension and biorthogonal multiwavelet construction

Suppose that P(z) and (P) over tilde(z) are two r x n matrices over the Laurent polynomial ring R[z], where r < n, which satisfy the identity P(z)(P) over tilde(z)* = I-r on the unit circle T. We develop an algorithm that produces two n x n matrices Q(z) and (Q) over tilde(z) over R[z], satisfying the identity Q(z)(Q) over tilde(z)* = I-n on T, such that the submatrices formed by the first r rows of Q(z) and (Q) over tilde(z) are P(z) and (P) over tilde(z) respectively. Our algorithm is used to construct compactly supported biorthogonal multiwavelets from multiresolutions generated by univariate compactly supported biorthogonal scaling functions with an arbitrary dilation parameter m is an element of E, where m > 1. (C) 1998 Elsevier Science Inc.