Results 151 to 160 of about 718 (189)

Balancing Regular Matrix Pencils

SIAM Journal on Matrix Analysis and Applications, 2006
We present a new diagonal balancing technique for regular matrix pencils $\lambda B-A$, which aims at reducing the sensitivity of the corresponding generalized eigenvalues. It is inspired by the balancing technique of a square matrix A and has a comparable complexity.
Paul Van Dooren
exaly   +2 more sources

Logarithmic Norms for Matrix Pencils

SIAM Journal on Matrix Analysis and Applications, 1999
Summary: The author extends the usual concepts of least upper bound norm and logarithmic norm of a matrix to matrix pencils. Properties of these seminorms and logarithmic norms are derived. This logarithmic norm can be used to study the growth of the solutions to linear variable coefficient differential-algebraic systems.
Inmaculada Higueras, Berta Garcia-Celayeta   +1 more
openaire   +1 more source

A QR Decomposition for Matrix Pencils

BIT Numerical Mathematics, 2000
An efficient and numerically stable modification of the \(QR\) decomposition for solving a linear least squares problem with a matrix of the form \(A+\lambda B\) is given. The idea is to proceed by columns and in step \(i\) the algorithm is driven by data from column \(i\) of the transformed matrices \(B\) and \(A\) in turn.
Spellucci, P., Hartmann, W. M.
openaire   +2 more sources

Arithmetic for rectangular matrix pencils

Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No.99TH8404), 2003
This paper is a generalization of the authors' (1998) previous study from square, regular n-by-n pencils to singular and rectangular m-by-n pencils. We define arithmetic-like operations on matrix pencils that are a natural extension of sums, products and quotients of real numbers.
Benner, P. ; https://orcid.org/0000-0003-3362-4103, Byers, R.   +1 more
openaire   +2 more sources

Combinatorial Analysis of Singular Matrix Pencils

SIAM Journal on Matrix Analysis and Applications, 2007
The structural approach to the analysis of singular matrix pencils is much more complicated than in the regular case because of nontrivial minimal row/column indices corresponding to the rectangular block in the canonical form. However, the main result of the paper under review provides a combinatorial characterization of the sums of the minimal row ...
Satoru Iwata 0001, Ryo Shimizu
openaire   +1 more source

On the Mahler measure of matrix pencils

2013 American Control Conference, 2013
It is well-known that determining the Mahler measure is important in networked control systems. Indeed, this measure allows one to derive stabilizability conditions in such systems. This paper investigates the Mahler measure in networked control systems linearly affected by a single uncertain parameter constrained into an interval, i.e.
openaire   +2 more sources

On the Canonical Forms of a Regular Matrix Pencil

Journal of Mathematical Sciences, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Evaluating products of matrix pencils and collapsing matrix products

Numerical Linear Algebra with Applications, 2001
AbstractThis paper describes three numerical methods to collapse a formal product ofppairs of matrices$$P=\mathop{\prod}\limits_{k=0}^{p-1} E_{k}^{-1}A_{k}$$down to the product of a single pairÊ−1Â. In the setting of linear relations, the product formally extends to the case in which some of theEk's are singular and it is impossible to explicitly form ...
Peter Benner, Ralph Byers
openaire   +2 more sources

A deflation method for regular matrix pencils

Applied Mathematics and Computation, 2011
A matrix pencil \(\lambda Y-X\) of order \(m\) is called an eigenpencil of a matrix pencil \(\lambda B-A\) or order \(n>m\) if there exist \(n\times m\) matrices \(V\) and \(W\) of rank \(m\) such that \((\lambda B-A)V=W(\lambda Y-X)\). The authors show that, if an eigenpencil is known, it may be used to extend the Wielandt deflation for regular matrix
Edgar Pereira, Cecilia Rosa
openaire   +3 more sources

Matrix pencil method and its performance

ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing, 2003
A novel method called matrix pencil method for estimating poles or frequencies from exponentially damped or undamped sinusoidal sequences is presented as an alternative to either the ESPRIT or pencil-of-functions method. A singular generalized eigenvalue problem in this method is solved in several different ways.
Yingbo Hua, Tapan K. Sarkar
openaire   +1 more source