Jacobi–Davidson methods for polynomial two-parameter eigenvalue problems

We propose Jacobi–Davidson type methods for polynomial two-parameter eigenvalue problems (PMEP). Such problems can be linearized as singular two-parameter eigenvalue problems, whose matrices are of dimension k(k+1)n/2, where k is the degree of the polynomial and n is the size of the matrix coefficients in the PMEP. When k2n is relatively small, the problem can be solved numerically by computing the common regular part of the related pair of singular pencils. For large k2n, computing all solutions is not feasible and iterative methods are required.