Interpolating self consistent field for eigenvector nonlinearities

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.