The Lanczos algorithm is one of the principal algorithms for the computation of a few of the extreme eigenvalues and their corresponding eigenvectors of very large, sparse, symmetric matrices and is currently the subject of intense research. In this paper two explicit restart techniques for the algorithm are proposed and their suitability for implementation in two different parallel environments is explored. Both techniques adopt a deflation approach in which exactly one eigenpair at a time is computed. Thus, p eigenpairs are computed using exactly p applications of the chosen Lanczos method. Newly generated Lanczos vectors are orthogona-lized with respect to all previously converged eigenvectors. Each of the techniques has been embedded in a version of the Lanczos algorithm which incorporates full reorthogonalization of the Lanczos vectors as well as a new convergence monitoring routine. Both of the modified Lanczos algorithms have been implemented in a distributed memory SIMD environment and in a shared...
['Marek Szularz', 'Jim Weston', 'Maurice Clint']
RESTARTING TECHNIQUES FOR THE LANCZOS ALGORITHM AND THEIR IMPLEMENTATION IN PARALLEL COMPUTING ENVIRONMENTS: ARCHITECTURAL INFLUENCES