Matrix Continued Fractions Original Research Article

A matrix continued fraction is defined and used for the approximation of a function F known as a power series in 1/zwith matrix coefficientsp×q, or equivalently by a matrix of functions holomorphic at infinity. It is a generalization of P-fractions, and the sequence of convergents converges to the given function. These convergents have as denominators a matrix, the columns of which are orthogonal with respect to the linear matrix functional associated to F. The case where the algorithm breaks off is characterized in terms of F.