Results 121 to 130 of about 9,941 (162)
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Logarithmic Norms for Matrix Pencils
SIAM Journal on Matrix Analysis and Applications, 1999Summary: 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 +1 more
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A QR Decomposition for Matrix Pencils
BIT Numerical Mathematics, 2000An 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.
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Balancing Regular Matrix Pencils
SIAM Journal on Matrix Analysis and Applications, 2006We 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.
Damien Lemonnier, Paul Van Dooren
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Rank One Perturbations of Matrix Pencils
SIAM Journal on Matrix Analysis and Applications, 2020Using some of their earlier results (see for example [the first author, Linear Algebra Appl. 438, No. 8, 3155--3173 (2013; Zbl 1269.15029)]), the authors completely resolve the open problem of describing all possible Kronecker invariants of an arbitrary matrix pencil under rank one perturbations.
Marija Dodig, Marko Stosic
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Arithmetic for rectangular matrix pencils
Proceedings of the 1999 IEEE International Symposium on Computer Aided Control System Design (Cat. No.99TH8404), 2003This 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 +1 more
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Combinatorial Analysis of Singular Matrix Pencils
SIAM Journal on Matrix Analysis and Applications, 2007The 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
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On the Mahler measure of matrix pencils
2013 American Control Conference, 2013It 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.
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On the Canonical Forms of a Regular Matrix Pencil
Journal of Mathematical Sciences, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Evaluating products of matrix pencils and collapsing matrix products
Numerical Linear Algebra with Applications, 2001AbstractThis 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
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