Application of Higham-Cheng Algorithm to the Generalized Eigenproblem in Computational Electromagnetics

The generalised eigenproblem Ax=λBx is very oftenencountered in computational electromagnetics. Its solution iseasily obtained when the matrices A and B are Hermitian and B ispositive definite. However, the errors introduced by thediscretisation process can deteriorate the properties of thematrices A and B in such a way that common techniques can nolonger be used. The Higham-Cheng algorithm is proposed as amethod to solve the generalised eigenproblem in these last cases.A brief account of the method is given and the algorithm isapplied to two classical electromagnetic problems.