A new algorithm for computing Pade approximants

Abstract

In paper a new definition of reduced Pade approximant and algorithm for its computing is proposed. Our approach is based on the investigation of the kernel structure of the Toeplitz matrix. It is shown that the reduced Pade approximant always has nice properties which classical Pade approximant possesses only in the normal case. The new algorithm allows us to avoid Froissart doublets appearance induced by computer roundoff in the non-normal Pade table.