Linearizable Eigenvector Nonlinearities

We present a method to linearize, without approximation, specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the are expressed by scalar functions that defined quotient linear eigenvector. The exact linearization relies on an equivalent multiparameter problem (MEP) contains solutions NEPv. Due characterization MEPs in terms generalized this provides direct way compute all NEPv for small problems, and it opens up possibility develop locally convergent iterative methods larger problems. Moreover, formulation allows us easily determine number propose two numerical schemes exploit structure linearization: inverse iteration residual iteration. show how symmetry MEP can be used improve reliability reduce computational cost both methods. Two examples verify theoretical results, third example shows potential hybrid scheme is based combination proposed