Interpolating self consistent field for eigenvector nonlinearities

Abstract

One of the most common approaches for solving eigenvalue problems with eigenvector nonlinearities (NEPv) is the Self Consistent Field (SCF) method that uses a vector from the previous iteration to build a zeroth order approximation of the nonlinearity. This approach is often slow and unreliable, which is why most applications use mixing scheme extensions of SCF, that use a linear combination of multiple previous iterates to build the zeroth order approximation. In this paper, we present a method that uses multiple previous iterates to build an interpolating first order approximation of the nonlinearity. It can be shown that this method converges superlinearly to the desired eigenpair.