A NOVEL ALGORITHM FOR CALCULATION OF THE EXTREME EIGENVALUES OF LARGEHERMITIAN MATRICES

A new fast algorithm for calculating a few maximum (or minimum) eigenv alues and the corresponding eigenvectors of large N X N Hermitian matr ices is presented, The method is based on a molecular dynamics algorit hm for N coupled harmonic oscillators. The time step for iteration is chosen so that only the normal mode with the maximum eigenvalue grows exponentially. Other eigenvalues and eigenvectors are obtained one by one from the largest eigenvalue by repeating the process in subspaces orthogonal to the previous modes. The characteristics of the algorithm lie in the simplicity, speed (CPU time is-proportional-to N2), and me mory efficiency (O(N) besides the matrix). The effectiveness of the al gorithm is illustrated by calculation of the groundstate and first-exc ited state energies of the Heisenberg model for an antiferromagnetic c hain with N up to 16384.