This paper describes a restarted Lanczos algorithm that particularly suitable for implementation on distributed machines. The only communication operation is requires outside of the matrix-vector multiplication is a global sum. For most large eigenvalue problems, the global sum operation takes a small fraction of the total execution time. The majority of the computer is spent in the matrix-vector multiplication. Efficient parallel matrix-vector multiplication routines can be found in many parallel sparse matrix packages such as AZTEC , BLOCK-SOLVE , PETSc , P-SPARSLIB1. For this reason, our main emphasis in this paper is to demonstrate the correctness and the effectiveness of the new algorithm.
Wu, K., & Simon, H. D. (1998). Thick-restart Lanczos method for symmetric eigenvalue problems. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1457 LNCS, pp. 43–55). Springer Verlag. https://doi.org/10.1007/bfb0018526