COMPUTATION OF NUMERICAL PADE-HERMITE AND SIMULTANEOUS PADE SYSTEMS .1. NEAR INVERSION OF GENERALIZED SYLVESTER MATRICES

We present new formulae for the ''near'' inverses of striped Sylvester and mosaic Sylvester matrices. The formulae assume computation over f loating-point rather than exact arithmetic domains. The near inverses are expressed in terms of numerical Pade-Hermite systems and simultane ous Pade systems. These systems are approximants for the power series determined from the coefficients of the Sylvester matrices. The invers e formulae provide good estimates for the condition numbers of these m atrices and serve as primary tools in a companion paper for the develo pment of a fast, weakly stable algorithm for the computation of Pade-H ermite and simultaneous Pade systems and, thereby, also for the numeri cal inversion of striped and mosaic Sylvester matrices.