  We propose a general numerical approach to open quantum systems with a
coupling to bath degrees of freedom. The technique combines the methodology of
polynomial expansions of spectral functions with the sparse grid concept from
interpolation theory. Thereby we construct a Hilbert space of moderate
dimension to represent the bath degrees of freedom, which allows us to perform
highly accurate and efficient calculations of static, spectral and dynamic
quantities using standard exact diagonalization algorithms. The strength of the
approach is demonstrated for the phase transition, critical behaviour, and
dissipative spin dynamics in the spin boson model
