A comparison of filter diagonalisation methods with the Lanczos method for calculating vibrational energy levels

In this Letter we compare two low-storage filter diagonalisation methods for calculating energy levels and compare both to the Lanczos algorithm. We are able to calculate energy levels in a high-lying window in the vibrational spectrum of H2O with fewer matrix–vector products using the Lanczos algorithm than using the filter diagonalisation methods. We find that the Lanczos calculation is less costly and that the cost of building the Hamiltonian and overlap matrices in the filtered basis is excessive if one uses a non-Chebyshev discrete variable representation filter.