  We propose a wave operator method to calculate eigenvalues and eigenvectors
of large parameter-dependent matrices, using an adaptative active subspace. We
consider a hamiltonian which depends on external adjustable or adiabatic
parameters, using adaptative projectors which follow the successive eigenspaces
when the adjustable parameters are modified. The method can also handle
non-hermitian hamiltonians. An iterative algorithm is derived and tested
through comparisons with a standard wave operator algorithm using a fixed
active space and with a standard block-Davidson method. The proposed approach
is competitive, it converges within a few dozen iterations at constant memory
cost. We first illustrate the abilities of the method on a 4-D coupled
oscillator model hamiltonian. A more realistic application to molecular
photodissociation under intense laser fields with varying intensity or
frequency is also presented. Maps of photodissociation resonances of H${}_2^+$
in the vicinity of exceptional points are calculated as an illustrative
example.
