Computing high precision Matrix Padé approximants

We describe a new method of computing matrix Padé approximants of series with integer data in an efficient and fraction‐free way, by controlling the growth of the size of intermediate coefficients. This algorithm is applied to compute high precision Padé approximants of matrix‐valued generating functions of time series. As an illustration we show that we can successfully recover from noisy equidistant sampling data a joint damped signal of four antenna, even in the presence of background signals.