A successive approximation method for solving equations of the second kind with arbitrary spectral radius

Author: Heinz W. Engl

Abstract: We derive a method for solving (I-K)x=y with compact K without assumptions on the spectral radius or on the multiplicity of the poles of the resolvent. The method combines successive approximation with a modified right-hand side and solving a certain finite-dimensional linear system. As a by-product, we obtain a Fredholm-type characterization of those right-hand sides for which the equation is solvable by iteration.