Multidimensional systems theory: Matrix pade approximants

In view of potential applications in several problems including the design of multi-input multi-output recursive digital filters from a prescribed sequence of impulse response matrices, and multiport network design, several problems in the theory of matrix Pade approximation are investigated. Results on the existence of solution to the approximation problem and a recursive scheme for computation of the approximant, when its existence is guaranteed, are arrived at. Links of this matrix approximation theory to the known results in the 1- D and 2-D scalar cases are pointed out. Emphasis here is on 1-D matrix Pade approximants, though the results arrived at, very recently, by the authors in the 2-D case are very briefly alluded to.