We show that the quantum dynamics of a system comprised of a subspace Q coupled to a much larger subspace P can be recast as a reduced set of ordinary differential equations with constant coefficients. These equations can be solved by a single diagonalization of a general complex matrix. The efficiency of the method is demonstrated via computations on large molecular systems, as the radiationless transitions in pyrazine. We also present a solution to the "Multi-Channel Quantum Control" problem, where selective and complete population transfer from an initial bound state to M energetically degenerate continuum channels is achieved. The control is affected by coherently controlled Adiabatic Passage proceeding via N bound intermediate states. We illustrate the viability of the method by computationally controlling the multi-channel photodissociation of methyl iodide.