Accuracy-through-order and the equivalence properties in the algebraic approximant.

摘要

In addition to the accuracy-through-order requirement that the defining polynomials not all be divisible by z, as required for Pade and integral approximants, there is the further problem of deficiency as pointed out by McInnes. I prove a finite bound on the deficiency and also prove the accuracy-through-order property for algebraic approximants. In addition I prove the equivalence property for algebraic approximants.