SOFTWARE FOR SIMPLIFIED LANCZOS AND QMR ALGORITHMS

The nonsymmetric Lanczos process simplifies when applied to J-symmetri c and J-Hermitian matrices, and work and storage requirements are roug hly halved compared to the general case. In this paper, we describe FO RTRAN-77 implementations of simplified versions of the look-ahead Lanc zos algorithm and of the quasiminimal residual (QMR) method, which is a Lanczos-based iterative procedure for the solution of linear systems . These implementations of the simplified algorithms complete our soft ware package QMRPACK, which so far contained only codes for Lanczos an d QMR algorithms for general matrices. We describe in some detail the use of two routines, one for the solution of linear systems, and the o ther for eigenvalue computations. We present examples that lead to J-s ymmetric and J-Hermitian matrices. Results of numerical experiments ar e reported.