The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis
William B. Gragg · SIAM Review · 1972
The algebraic theory of the Padé table of a formal power series is presented with a natural notation which indicates possible extensions to Laurent series. The theory is related to bigradient determinants, the epsilon and eta algorithms, and to a variant of the quotient-difference algorithm. Normality criteria for the Padé table, which provide existence theorems for the algorithms, are developed.