Applicability of the Newton-Kantorovich method and optimization theory to dispersion relations of the Chew-Mandelstam type

Abstract

The mathematical structure of the Chew-Mandelstam type dispersion relations is examined to determine if the Newton-Kantorovich method of solution can be applied. Constructive methods for finding the solutions without the N/D factorization are worked out. Our numerical techniques for solving non-linear integral equations with Cauchy kernels on the basis of the Newton-Kantorovich method and our optimization procedure are applicable to a wide variety of problems in the S-matrix theory. © 1969.