Nearest Definite Pair for the Generalized Eigenproblem Applied to the Computation of the Characteristic Modes

In electromagnetics many problems are rapresentable in the form Ax=lBx in which the pair (A,B) is hermitian and B is positive definite. These problems are resoluble by simultaneous diagonalization of the pair (A,B). Because of numerical aproximation and rounding sometimes it may be happen that the proprieties of the pair deteriorate and the simultaneous diagonalization procedure results inapplicable. In this work a new technique developed recently by Higham and Cheng based on the calculation of the nearest definite pair is proposed as a method to solve these last cases. It is applied to the computation of the characteristic modes for the plane wave scattering from a conducting elliptic cylinder and from an array of two L shaped microstrip patches. Results are analyzed and discussed.