Solution of Linear Integral Equations Using Padé Approximants

Abstract

It is shown that the exact solution of a nonhomogeneous linear integral equation with a kernel K of rank n is given by forming the Padé approximant P(n, n) from the first 2n terms of the perturbation series solution. It follows that for a compact kernel K, the solution is lim_n→∞ P(n, n); this gives meaning to a large class of perturbation series when the perturbation is large. The possible extension of this result to wider classes of equations is discussed.