Comparison of Chebyshev, Faber, and Lanczos propagation-based methods for calculating resonances

We compare the numerical performance of three recursive methods for calculating collisional resonances, which are characterized by complex eigenenergies of an optical potential augmented Hamiltonian. The first approach involves a modified Chebyshev propagation of a real wave packet, followed by low-storage filter-diagonalization. A similar filter-diagonalization scheme replaces the Chebyshev propagation with a more general Faber recursion associated with a specific conformal mapping in the complex plane. The complex resonance eigenenergies are also obtained using a complex-symmetric version of the Lanczos algorithm. Numerical tests for a realistic triatomic system (HCO) indicate that the Lanczos method and the low-storage filter-diagonalization based on the Chebyshev propagation are much more efficient than the Faber approach. (C) 2000 American Institute of Physics. [S0021-9606(00)00412-8].