A $QL$ Procedure for Computing the Eigenvalues of Complex Symmetric Tridiagonal Matrices
Jane K. Cullum, Ralph A. Willoughby · SIAM Journal on Matrix Analysis and Applications · 1996
We present a storage efficient procedure for computing all of the eigenvalues of a complex symmetric tridiagonal matrix. This procedure mimics the implicit $QL$ procedure for computing all of the eigenvalues of a real symmetric tridiagonal matrix, modified by heuristics for monitoring and maintaining numerical stability. Numerical experiments demonstrate the capabilities of this procedure.