Efficient calculation of matrix elements in low storage filter diagonalization

Efficient extraction of frequency information from a discrete sequence of time signals can be achieved using the so-called low storage filter diagonalization approach. This is possible because the signal sequence can be considered as a correlation function associated with a quantum Hamiltonian. The eigenvalues of the Hamiltonian (i.e., the frequencies in the signal) in a pre-specified energy range are obtainable from a low-rank generalized eigenequation in a subspace spanned by the filtered states. This work presents an efficient and accurate method to construct the Hamiltonian and overlap matrices directly from correlation functions for several types of propagators. Emphasis is placed on a recurrence relationship between the Hamiltonian and overlap matrices. This method is similar to, but more efficient than, several existing methods. Numerical testing in a triatomic system (HOCl) confirms its accuracy and efficiency. (C) 1999 American Institute of Physics. [S0021-9606(99)00926-5].