Implicit algorithms for eigenvector nonlinearities

Abstract We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on eigenvector, or several eigenvectors (or their corresponding invariant subspace). The are derived from an implicit viewpoint. More precisely, we change Newton update equation in a way that next iterate does not only appear linearly equation. Although modifications of make methods implicit, show how iterates can be computed explicitly. Therefore, carry out steps method using explicit procedures. In cases, these procedures involve solution standard problems. propose two modifications, one leads directly to well-established (the self-consistent field iteration) whereas other is our knowledge new has attractive properties. Convergence theory provided along with simulations which illustrate properties algorithms.