Jacobi-Davidson Algorithm with Fast Matrix-Vector Multiplikation on Massively Parallel and Vector Supercomputers

The exact diagonalization of very large sparse matrices is a numerical problem common to various fields in science and engineering. We present an advanced eigenvalue alorithm - the so-called Jacobi-Davidson algorithm - in combination with an efficient parallel matrix-vector multiplication. This implementation allows the calculation of several specified eigenvalues with high accuracy on modern supercomputers, such as CRAY T3E and NEC SX-4. Exemplarily the numerical technique is applied to analyze the ground state and spectral properties of the three-quarter filled Peierls-Hubbard Hamiltonian in relation to recent resonant Raman experiments on MX chain [-PtCl-] complexes.