Abstract
Quantum resonances described by non-Hermitian tridiagonal-matrix Hamiltonians H with complex energy eigenvalues are considered. The method of evaluation of quantities σ_n known as the singular values of H is proposed. Its basic idea is that the quantities σ_n can be treated as eigenvalues of an auxiliary self-adjoint operator H. As long as such an operator can be given a block-tridiagonal matrix form, we finally expand its resolvent in terms of a matrix continued fraction (MCF). In an illustrative application, a discrete version of conventional Hamiltonian H=-d²/dx²+V(x) with complex local V(x) ≠ V^*(x) is considered. The numerical MCF convergence is found quick, supported also by a fixed-point-based formal proof.