A generalized complex symmetric eigensolver

Abstract

For a heavily damped system, either viscous or hysteresis or both, the homogeneous solution constitutes a generalized complex symmetric eigenproblem [A]{x}= λ [B]{x}, where [A] and [B]are complex symmetric matrices. The general complex method to solve the transformed eigenproblem [B] su−1 [A]{x} = λ {x} is very demanding in computation. A new method of Jacobi rotation is introduced to solve the complex symmetry eigenproblem completely. Full advantages of the symmetry are taken. The complex eigenvalues can be computed directly when both matrices are diagonalized. The complex eigenvectors are obtained as the products of the complex plane rotation. A Fortran subroutine and examples are given.