SLICOT Working Note 2013-3 MB04BV A FORTRAN 77 Subroutine to Compute the Eigenvectors Associated to the Purely Imaginary Eigenvalues of Skew-Hamiltonian/Hamiltonian Matrix Pencils
نویسندگان
چکیده
We implement a structure-preserving numerical algorithm for extracting the eigenvectors associated to the purely imaginary eigenvalues of skew-Hamiltonian/Hamiltonian matrix pencils. We compare the new algorithm with the QZ algorithm using random examples with di erent di culty. The results show that the new algorithm is signi cantly faster, more robust, and more accurate, especially for hard examples.
منابع مشابه
FORTRAN 77 Subroutines for the Solution of Skew-Hamiltonian/Hamiltonian Eigenproblems - Part II: Implementation and Numerical Results
Skew-Hamiltonian/Hamiltonian matrix pencils λS −H appear in many applications, including linear quadratic optimal control problems, H∞-optimization, certain multi-body systems and many other areas in applied mathematics, physics, and chemistry. In these applications it is necessary to compute certain eigenvalues and/or corresponding deflating subspaces of these matrix pencils. Recently develope...
متن کاملFortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices II
This article describes Fortran 77 subroutines for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices. The implemented algorithms are based on orthogonal symplectic decompositions, implying numerical backward stability as well as symmetry preservation for the computed eigenvalues. These algorithms are supplemented with balancing and block algorithms, which...
متن کاملFortran 77 Subroutines for Computing the Eigenvalues of Hamiltonian Matrices I: the Square Reduced Method
This paper describes LAPACK-based Fortran 77 subroutines for the reduction of a Hamiltonian matrix to square-reduced form and the approximation of all its eigenvalues using the implicit version of Van Loan's method. The transformation of the Hamiltonian matrix to a square-reduced form transforms a Hamiltonian eigenvalue problem of order 2n to a Hessenberg eigenvalue problem of order n. The eige...
متن کاملOn Computing Stable Lagrangian Subspaces of Hamiltonian Matrices and Symplectic Pencils∗
This paper presents algorithms for computing stable Lagrangian invariant subspaces of a Hamiltonian matrix and a symplectic pencil, respectively, having purely imaginary and unimodular eigenvalues. The problems often arise in solving continuousor discrete-time H∞-optimal control, linear-quadratic control and filtering theory, etc. The main approach of our algorithms is to determine an isotropic...
متن کاملEla Perturbation of Purely Imaginary Eigenvalues of Hamiltonian Matrices under Structured Perturbations∗
The perturbation theory for purely imaginary eigenvalues of Hamiltonian matrices under Hamiltonian and non-Hamiltonian perturbations is discussed. It is shown that there is a substantial difference in the behavior under these perturbations. The perturbation of real eigenvalues of real skew-Hamiltonian matrices under structured perturbations is discussed as well and these results are used to ana...
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 2013