LARGE MATRIX DIAGONALIZATION, COMPARISON OF VARIOUS ALGORITHMS AND A NEW PROPOSAL

We compare various algorithms for large matrix diagnalization, namely the Davidson and Olsen-Davidson algorithms, and a Lanczos-like one, as well as a new method introduced here. The numerical tests are perform ed with the help of a model involving a vibronic Hamiltonian and a bat h. For various cases, it is shown that the convergence of the Davidson and Olsen-Davidson methods is sensitive to the adequacy of the trial vector. The new method presents convergence properties similar to the Davidson and Olsen-Davidson methods in their most favorable case, but thes convergence properties are not destroyed by a poor guess of the t rial vector.