Analysis of the lagrange multipliers method using the technique of analytical integration applied to waveguides

The cutoff frequencies of the rectangular waveguides are calculated using the technique of the Lagrange Multipliers. The application of the technique of analytical integration is made with the integrals written in the homogeneous coordinates of the finite element. The final system is badly conditioned, symmetrical and is not defined positive. We present a form to turn it out to be defined positive.