Higham-Cheng algorithm for solving the generalized eigenproblem applied to the computation of the characteristic modes

In computational electromagnetics many problems are representable in the form Ax = /spl lambda/Bx where the matrices A, B are Hermitian and B is positive definite. These problems are solvable with high accuracy by the simultaneous diagonalization of the pair (A, B). However, it may happen that numerical approximations and rounding errors deteriorate the properties of the pair (A, B) in a way that the simultaneous diagonalization procedure results are inapplicable. In this work a new algorithm developed recently by Higham and Cheng (1999) is proposed as a method to be applied in these cases. In particular, the computation of the characteristic modes for the TM/sub 2/, scattering by a conducting elliptic cylinder is addressed, and results are analyzed and discussed.