Eigenvalues of the moment-method matrix and their effect on the convergence of the conjugate gradient algorithm (EM scattering)

Abstract

A theory that relates eigenvalues of a continuous operator to those of the moment-method matrix operator is discussed and confirmed by examples. This theory suggests reasons for ill conditioning when certain types of basis and testing functions are used. In addition, the effect of eigenvalue location on the convergence of the conjugate gradient (CG) method is studied. The convergence rate of the CG method is dependent on the eigenvalues of the iteration matrix as well as on the number of eigenvectors of the iteration matrix needed to represent the right side of the equation. These findings explain the previously reported convergence behavior of the CG method when applied to electromagnetic-scattering problems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>