MATRIX EXTENSION AND BIORTHOGONAL MULTIWAVELET CONSTRUCTION

Suppose that P(z) and (P) over tilde(z) are two r x n matrices over th e Laurent polynomial ring R[z], where r < n, which satisfy the identit y P(z)(P) over tilde(z) = I-r on the unit circle T. We develop an alg orithm that produces two n x n matrices Q(z) and (Q) over tilde(z) ove r R[z], satisfying the identity Q(z)(Q) over tilde(z) = I-n on T, suc h 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 i s used to construct compactly supported biorthogonal multiwavelets fro m multiresolutions generated by univariate compactly supported biortho gonal scaling functions with an arbitrary dilation parameter m is an e lement of E, where m > 1. (C) 1998 Elsevier Science Inc.