Use of the Simultaneous Diagonalization Technique in the Ax=λBx Eigenproblem Applied to the Computation of the Characteristic Modes

Characteristic modes developed byGarbacz, Harrington and Mautz have long beenused in the analysis of radiation and scatteringfrom conducting bodies and apertures. For theircomputation, it is necessary to solve an eigen-system of the form Ax=λBx. If the matrices (A, B) are Hermitian and B is positive definite, the generalized eigenvalue problem can be accurately solved using the simultaneous diagonalization technique (SDT). Because of numericalapproximations and rounding sometimes it mayhappen that the matrices properties deteriorateand the SDT procedure becomes inapplicable.In this work a new technique, developed recentlyby Higham and Cheng is proposed as a methodto solve these deteriorate cases. It is applied tothe computation of the characteristic modes forsome scattering problems. Results are analyzedand discussed.