TY - JOUR

T1 - A symmetric structure-preserving ΓQR algorithm for linear response eigenvalue problems

AU - Li, Tiexiang

AU - Li, Ren Cang

AU - Lin, Wen-Wei

PY - 2017/5/1

Y1 - 2017/5/1

N2 - In this paper, we present an efficient ΓQR algorithm for solving the linear response eigenvalue problem Hx=λx, where H is Π−-symmetric with respect to Γ0=diag(In,−In). Based on newly introduced Γ-orthogonal transformations, the ΓQR algorithm preserves the Π−-symmetric structure of H throughout the whole process, and thus guarantees the computed eigenvalues to appear pairwise (λ,−λ) as they should. With the help of a newly established implicit Γ-orthogonality theorem, we incorporate the implicit multi-shift technique to accelerate the convergence of the ΓQR algorithm. Numerical experiments are given to show the effectiveness of the algorithm.

AB - In this paper, we present an efficient ΓQR algorithm for solving the linear response eigenvalue problem Hx=λx, where H is Π−-symmetric with respect to Γ0=diag(In,−In). Based on newly introduced Γ-orthogonal transformations, the ΓQR algorithm preserves the Π−-symmetric structure of H throughout the whole process, and thus guarantees the computed eigenvalues to appear pairwise (λ,−λ) as they should. With the help of a newly established implicit Γ-orthogonality theorem, we incorporate the implicit multi-shift technique to accelerate the convergence of the ΓQR algorithm. Numerical experiments are given to show the effectiveness of the algorithm.

KW - Linear response eigenvalue problem

KW - Structure preserving

KW - Γ-orthogonality

KW - ΓQR algorithm

KW - Π-matrix

UR - http://www.scopus.com/inward/record.url?scp=85010203612&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2017.01.005

DO - 10.1016/j.laa.2017.01.005

M3 - Article

AN - SCOPUS:85010203612

VL - 520

SP - 191

EP - 214

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -