For the solution of the SID (Symmetric InDefinite) linear systems, the use of the GLS (Generalized Least-Squares) polynomial preconditioner can improve the execution efficiency of solvers, particularly for some specially structured systems. In this paper the suitability of GLS preconditioning for a class of specially structured linear system of equations is demonstrated. The algorithms are implemented using MPI in a highly parallel IBM SP2 environment and experimental results are presented. The performance of the GLS preconditioned FGMRES solver and the eigensolver based on it is critically assessed.