Nonlinearizing Two-parameter Eigenvalue Problems

We investigate a technique to transform linear two-parameter eigenvalue problem into nonlinear (NEP). The transformation stems from an elimination of one the equations in problem, by considering it as (standard) generalized problem. characterize equivalence between original and nonlinearized theoretically show how use computationally. Special cases can be interpreted reversed companion linearization for polynomial problems, well (less known) certain algebraic problems with square-root terms. Moreover, exploiting structure NEP we present algorithm specializations methods, although also allows general solution methods NEPs directly applied. nonlinearization is illustrated examples simulations, focus on where eliminated equation much smaller size than other equation. This situation arises naturally domain decomposition techniques. A error analysis carried out under assumption that backward stable eigensolver used solve leading conclusion benign this situation.