A two-dimensional matrix Padé-type approximation in the inner product space

By introducing a bivariate matrix-valued linear functional on the scalar polynomial space, a general two-dimensional (2-D) matrix Padé-type approximant ( B M P T A ) in the inner product space is defined in this paper. The coefficients of its denominator polynomials are determined by taking the direct inner product of matrices. The remainder formula is developed and an algorithm for the numerator polynomials is presented when the generating polynomials are given in advance. By means of the Hankel-like coefficient matrix, a determinantal expression of B M P T A is presented. Moreover, to avoid the computation of the determinants, two efficient recursive algorithms are proposed. At the end the method of B M P T A is applied to partial realization problems of 2-D linear systems.