An analysis of two variable rational approximants

摘要

We present two determinants whose ratio is the Hughes Jones approximant to a power series in two variables. They are generalizations of Jacobi's determinants for Padé approximants. They are useful in certain circumstances when the defining equations are degenerate. We analyze the indeterminacies associated with degenerate approximants, at least one of which is quite different in nature from the degeneracies of the single variable Padé approximants. We are led to suggest a modification of the symmetrizing equations which leads to numerical stability.