The determination of several interior eigensolutions of large non-hermitian matrices is still an open problem for research. This paper brings significant improvements to the perturbative iterative methods. The theory is developed in the framework of Bloch formalism of wave operators and effective Hamiltonians. The progresses rely on two factors. First, the full Hilbert space is partitioned into three subspaces to improve the convergence and stability properties of the iterative processes. Second, the quasi-quadratic algorithms are well-defined approximations of the exact quadratic Newton-Raphson solution. The addition of these two factors brings the computational efficiency far beyond standard perturbation theory. An application is presented to the determination of the Floquet resonances arising from the ten lowest vibrational states of the molecular ion H-2(+) for laser intensities up to 1.6x10(15) W cm(-2). These Floquet states provide the relevant basis of the dynamics of H-2(+) submitted to intense laser pulses.