Some remarks on the complex &ITJ&IT-symmetric eigenproblem

被引：11

作者：

Benner, Peter ^{[1
]}

Fassbender, Heike ^{[2
]}

Yang, Chao ^{[3
]}

机构：

[1] Max Planck Inst Dynam Complex Tech Syst, Sandtorstr 1, D-39106 Magdeburg, Germany

[2] TU Braunschweig, AG Numer, Univ Pl 2, D-38106 Braunschweig, Germany

[3] Lawrence Berkeley Natl Lab, Computat Res Div, Berkeley, CA 94720 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2018年 / 544卷

关键词：

Complex J-symmetric eigenproblem; Real Hamiltonian matrix; Complex Hamiltonian matrix; Structure-preserving; SR algorithm; EIGENVALUE PROBLEM; HAMILTONIAN MATRICES; ALGORITHMS; FACTORIZATIONS; DECOMPOSITION; CONVERGENCE;

D O I：

10.1016/j.laa.2018.01.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The eigenproblem for complex J-symmetric matrices H-C = [GRAPHICS], A, C = C-T, D = D-T is an element of C-nxn is considered. A proof of the existence of a transformation to the complex J-symmetric Schur form proposed in [21] is given. The complex symplectic unitary QR decomposition and the complex symplectic SR decomposition are discussed. It is shown that a QR-like method based on the complex symplectic unitary QR decomposition is not feasible here. A complex symplectic SR algorithm is presented which can be implemented such that one step of the SR algorithm can be carried out in O(n) arithmetic operations. Based on this, a complex symplectic Lanczos method can be derived. Moreover, it is discussed how the 2n x 2n complex J-symmetric matrix H-C can be embedded in a 4n x 4n real Hamiltonian matrix. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：407 / 442

页数：36

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