Modified explicitly restarted Lanczos algorithm Original Research Article

We propose a modified explicitly restarted Lanczos algorithm to calculate the eigenvalues and eigenvectors of large sparse matrices. There are at least four interesting features of this algorithm; (1) it can calculate multiplicities of matrices; (2) the convergence is rapid, especially for those hardly converged eigenstates. Thus the threshold can be set high, up to 10−14; (3) the implementation is extremely simple; (4) the required memory space is small. This new algorithm has been extensively tested and used in extended Hubbard chains.