Locating coalescing singular values of large two-parameter matrices

Consider a matrix valued function A(x)∈Rm×n, m ≥ n  , smoothly depending on parameters x∈Ω⊂R2, where Ω is simply connected and bounded. We consider a technique to locate parameter values where some of the q dominant (q ≤ n) singular values of A coalesce, in the specific case when A is large and m > n ≫ q.