Application of Higham-Cheng algorithm to the generalised eigenproblem in computational electromagnetics

The generalised eigenproblem Ax¯=λBx¯ is very often encountered in computational electromagnetics. Its solution is easily obtained when the matrices A and B are Hermitian and B is positive definite. However, the errors introduced by the discretisation process can deteriorate the properties of the matrices A and B in such a way that common techniques can no longer be used. The Higham-Cheng algorithm is proposed as a method to solve the generalised eigenproblem in these last cases. A brief account of the method is given and the algorithm is applied to two classical electromagnetic problems