On the convergence of numerical results in modal analysis

Previous studies of the relative convergence (RC) phenomenon in modal analysis showed the need to introduce the edge condition by using an explicit asymptotic behavior of modal coefficients. We do not agree that the edge condition is the only means of uniquely defining a solution. It is demonstrated that the RC can be avoided by including only the bounded feature of modal coefficients. The analytical computations are given in solving the bifurcated parallel plate waveguide. To solve the general problem of convergence of numerical results, a-proof is given of this convergence in modal analysis. The required condition is the use of a "well-conditioned" linear system. With this demonstration, the use of the condition number as purely numerical criterion is justified to ensure the convergence of results.