Software for simplified Lanczos and QMR algorithms Original Research Article

The nonsymmetric Lanczos process simplifies when applied to J-symmetric and J-Hermitian matrices, and work and storage requirements are roughly halved compared to the general case. In this paper, we describe FORTRAN-77 implementations of simplified versions of the look-ahead Lanczos 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 software package QMRPACK, which so far contained only codes for Lanczos and QMR algorithms for general matrices. We describe in some detail the use of two routines, one for the solution of linear systems, and the other for eigenvalue computations. We present examples that lead to J-symmetric and J-Hermitian matrices. Results of numerical experiments are reported.