A stabilization criterion for matrix pencils under bilinear transformation
نویسندگان
چکیده
منابع مشابه
A Stabilization Criterion for Matrices
Given a simple linear system ẋ(t) = Ax(t) which is unstable in the sense that A has eigenvalues in the open left half of the complex plane, it is shown how the system can be dilated to a stable system of larger size. The cases of real matrices and complex matrices are considered separately.
متن کاملA QR-Decomposition for Matrix Pencils
This paper describes an eecient and numerically stable modiication of the QR decomposition for solving a parametric set of linear least squares problems with a parametric matrix A+B for several values of the parameter. The method is demonstrated on a typical application.
متن کاملAn Arithmetic for Matrix Pencils
We deene an algebra on matrix pencils that is a natural extension of sums, products and quotients of real numbers. The classical algebra of linear transformations may be regarded as a special case of the algebra of pencils. The sum and product deened here preserve right deeating subspaces. We show below that the matrix sign function and the inverse-free algorithms can be derived from an algebra...
متن کاملPerturbation Theory for Rectangular Matrix Pencils Perturbation Theory for Rectangular Matrix Pencils
abstract The theory of eigenvalues and eigenvectors of rectangular matrix pencils is complicated by the fact that arbitrarily small perturbations of the pencil can cause them disappear. However, there are applications in which the properties of the pencil ensure the existence of eigen-values and eigenvectors. In this paper it is shown how to develop a perturbation theory for such pencils. ABSTR...
متن کاملBalancing Regular Matrix Pencils
In this paper we present a new diagonal balancing technique for regular matrix pencils λB − A, which aims at reducing the sensitivity of the corresponding generalized eigenvalues. It is inspired from the balancing technique of a square matrix A and has a comparable complexity. Upon convergence, the diagonally scaled pencil has row and column norms that are balanced in a precise sense. We also s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2008
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.01.013