nu-TRLan User Guide Version 1.0: A High-Performance Software Package for Large-Scale Harmitian Eigenvalue Problems

摘要

The original software package TRLan, (TRLan User Guide), page 24, implements the thick restart Lanczos method, (Wu and Simon 2001), page 24, for computing eigenvalues (lambda) and their corresponding eigenvectors v of a symmetric matrix A: Av = (lambda)v. Its effectiveness in computing the exterior eigenvalues of a large matrix has been demonstrated, (LBNL-42982), page 24. However, its performance strongly depends on the user-specified dimension of a projection subspace. If the dimension is too small, TRLan suffers from slow convergence. If it is too large, the computational and memory costs become expensive. Therefore, to balance the solution convergence and costs, users must select an appropriate subspace dimension for each eigenvalue problem at hand. To free users from this difficult task, nu-TRLan, (LNBL-1059E), page 23, adjusts the subspace dimension at every restart such that optimal performance in solving the eigenvalue problem is automatically obtained. This document provides a user guide to the nu-TRLan software package. The original TRLan software package was implemented in Fortran 90 to solve symmetric eigenvalue problems using static projection subspace dimensions. nu-TRLan was developed in C and extended to solve Hermitian eigenvalue problems.