Iteration method to determine the eigenvalues and eigenvectors of a target multiplet including full mode coupling

Global 3-D Earth structure has been widely studied using spectra of free oscillations. Here we present a new algorithm for the calculation of synthetic spectra, which gives results that are in principle exact, while avoiding decomposition of the very large coupling matrices needed by previous methods. This new method is similar to the subspace projection method, but can be iterated as many times as needed in order to completely represent the exact solution. The new method is more general than the subspace method though, as it works for non-hermitian and non-linear systems, hence attenuation and dispersion can easily be included. We show that one iteration is often sufficiently close to the exact solution. It also works very well for along-branch coupling, an important phenomenon for fundamental mode surface waves.