On the Reduction of a Hamiltonian Matrix to Hamiltonian Schur Form
نویسنده
چکیده
Recently Chu, Liu, and Mehrmann developed an O(n3) structure preserving method for computing the Hamiltonian real Schur form of a Hamiltonian matrix. This paper outlines an alternate derivation of the method and alternate explanation of why the method works. Our approach places emphasis eigenvalue swapping and relies less on matrix manipulations.
منابع مشابه
An iterative method for the Hermitian-generalized Hamiltonian solutions to the inverse problem AX=B with a submatrix constraint
In this paper, an iterative method is proposed for solving the matrix inverse problem $AX=B$ for Hermitian-generalized Hamiltonian matrices with a submatrix constraint. By this iterative method, for any initial matrix $A_0$, a solution $A^*$ can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of...
متن کاملPerturbation Analysis of Hamiltonian Schur and Block-Schur Forms
In this paper we present a complete perturbation analysis for the Hamiltonian Schurform of a Hamiltonian matrix under similarity transformations with unitary symplectic matrices.Both linear asymptotic and non-linear perturbation bounds are presented. The same analysis isalso carried out for two less condensed block-Schur forms. It suggests that the block forms areless sensitive ...
متن کاملNumerical Computation of Deflating Subspaces of Skew-Hamiltonian/Hamiltonian Pencils
We discuss the numerical solution of structured generalized eigenvalue problems that arise from linear-quadratic optimal control problems, H∞ optimization, multibody systems, and many other areas of applied mathematics, physics, and chemistry. The classical approach for these problems requires computing invariant and deflating subspaces of matrices and matrix pencils with Hamiltonian and/or ske...
متن کاملDilations, models, scattering and spectral problems of 1D discrete Hamiltonian systems
In this paper, the maximal dissipative extensions of a symmetric singular 1D discrete Hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the Hilbert space ℓ_{Ω}²(Z;C²) (Z:={0,±1,±2,...}) are considered. We consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. For each of these cases we establish a self...
متن کاملA new block method for computing the Hamiltonian Schur form
A generalization of the method of Chu, Liu and Mehrmann [7] for the computation of the Hamiltonian real Schur form is presented. The new method avoids some of the difficulties that may arise when a Hamiltonian matrix has tightly clustered groups of eigenvalues. A detailed analysis of the method is presented and several numerical examples demonstrate the superior behavior of the method.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006