A symmetric structure-preserving FQR algorithm for linear response eigenvalue problems

Abstract

In this paper, we present an efficient PQR algorithm for solving the linear response eigenvalue problem H-x = lambda(x) , where H is Pi(-)-symmetric with respect to Gamma(0) = diag(I-n,-I-n). Based on newly introduced Gamma-orthogonal transformations, the PQR algorithm preserves the Pi(-)-symmetric structure of H throughout the whole process, and thus guarantees the computed eigenvalues to appear pairwise (lambda, -lambda) as they should. With the help of a newly established implicit Gamma-orthogonality theorem, we incorporate the implicit multi-shift technique to accelerate the convergence of the Gamma QR algorithm. Numerical experiments are given to show the effectiveness of the algorithm.(C) 2017 Elsevier Inc. All rights reserved.