Recursive approximation of the dominant eigenspace of an indefinite matrix

We consider here the problem of tracking the dominant eigenspace of an indefinite matrix by updating recursively a rank k approximation of the given matrix. The tracking uses a window of the given matrix, which increases at every step of the algorithm. Therefore, the rank of the approximation increases also, and hence a rank reduction of the approximation is needed to retrieve an approximation of rank k. In order to perform the window adaptation and the rank reduction in an efficient manner, we make use of a new antitriangular decomposition for indefinite matrices. All steps of the algorithm only make use of orthogonal transformations, which guarantees the stability of the intermediate steps. We also show some numerical experiments to illustrate the performance of the tracking algorithm.