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 -