A new multidimensional rational approximant

Abstract

A new Pade-type rational approximant for a power series in two variables matched at the nodal points of a raster structure different from both Chisholm and Bose & Basu is developed. It becomes easier to define n-D rational approximants of a power series in n-variables for our choice of modal points of n-D raster structure which can be reduced to Pade approximants in one variable and Pade-type rational approximants in (n-k) variables. Unlike Chisholm's approximants no special constraints are imposed to obtain these unique rational approimant for 'normal case'. All the properties satisfied by Chisholm's approximants are also satisfied by the new approximants.