Výsledky vyhledávání - "D. Steven Mackey"

Minimal indices and minimal bases via filtrations

Autor: D. Steven Mackey

Publikováno v: The Electronic Journal of Linear Algebra. 37:276-294

A new way to formulate the notions of minimal basis and minimal indices is developed in this paper, based on the concept of a filtration of a vector space. The goal is to provide useful new tools for working with these important concepts, as well as

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::7c926ae3018abc475c32bc1b34cccb84
https://doi.org/10.13001/ela.2021.5971

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Quadratic realizability of palindromic matrix polynomials

Autor: Froilán M. Dopico, Vasilije Perović, D. Steven Mackey, Fernando De Terán

Publikováno v: e-Archivo. Repositorio Institucional de la Universidad Carlos III de Madrid
instname
e-Archivo: Repositorio Institucional de la Universidad Carlos III de Madrid
Universidad Carlos III de Madrid (UC3M)

Let $\cL = (\cL_1,\cL_2)$ be a list consisting of a sublist $\cL_1$ of powers of irreducible (monic) scalar polynomials over an algebraically closed field $\FF$, and a sublist $\cL_2$ of nonnegative integers. For an arbitrary such list $\cL$, we give

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2148a59bd9df271be9f8c5f6837b0874
https://doi.org/10.1016/j.laa.2019.01.003

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Van Dooren's Index Sum Theorem and Rational Matrices with Prescribed Structural Data

Autor: Froilán M. Dopico, D. Steven Mackey, Richard Hollister, Luis Miguel Anguas

The structural data of any rational matrix R(\lambda ), i.e., the structural indices of its poles and zeros together with the minimal indices of its left and right nonespaces, is known to satisfy a simple condition involving certain sums of these ind

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::434c756bad180bf2abe1860ba0d748e4
https://doi.org/10.1137/18m1171370

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Linearizations of matrix polynomials in Newton bases

Autor: D. Steven Mackey, Vasilije Perović

Publikováno v: Linear Algebra and its Applications. 556:1-45

We discuss matrix polynomials expressed in a Newton basis, and the associated polynomial eigenvalue problems. Properties of the generalized ansatz spaces associated with such polynomials are proved directly by utilizing a novel representation of penc

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b282b7511aaa872f330208678ec20f34
https://doi.org/10.1016/j.laa.2018.06.030

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Möbius transformations of matrix polynomials

Autor: D. Steven Mackey, Christian Mehl, Niloufer Mackey, Volker Mehrmann

Publikováno v: Linear Algebra and its Applications. 470:120-184

We discuss Mobius transformations for general matrix polynomials over arbitrary fields, analyzing their influence on regularity, rank, determinant, constructs such as compound matrices, and on structural features including sparsity and symmetry. Resu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b330fc2483a019e7d909e9e1f8c32b69
https://doi.org/10.1016/j.laa.2014.05.013

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The continuing influence of Fiedler’s work on companion matrices

Autor: D. Steven Mackey

Publikováno v: Linear Algebra and its Applications. 439:810-817

This is a reconstruction in article-like form of a talk given at the ``Minisymposium in Honor of Miroslav Fiedler'' at the 17th ILAS Conference, held at TU Braunschweig, Germany, on Thurs 25 Aug 2011.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::795f40695fdbcc2f34f3ef2bd210c533
https://doi.org/10.1016/j.laa.2011.11.002

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Skew-symmetric matrix polynomials and their Smith forms

Autor: D. Steven Mackey, Christian Mehl, Volker Mehrmann, Niloufer Mackey

Publikováno v: Linear Algebra and its Applications. 438:4625-4653

We characterize the Smith form of skew-symmetric matrix polynomials over an arbitrary field $\F$, showing that all elementary divisors occur with even multiplicity. Restricting the class of equivalence transformations to unimodular congruences, a Smi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b3ea54a34f762ce1b5b116a520193aa9
https://doi.org/10.1016/j.laa.2013.02.010

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Fiedler companion linearizations for rectangular matrix polynomials

Autor: Fernando De Terán, Froilán M. Dopico, D. Steven Mackey

Publikováno v: Linear Algebra and its Applications. 437(3):957-991

The development of new classes of linearizations of square matrix polynomials that generalize the classical first and second Frobenius companion forms has attracted much attention in the last decade. Research in this area has two main goals: finding

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::537cef69a8016f81a13180c37136f380

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Palindromic companion forms for matrix polynomials of odd degree

Autor: Froilán M. Dopico, D. Steven Mackey, Fernando De Terán

Publikováno v: Journal of Computational and Applied Mathematics. 236:1464-1480

The standard way to solve polynomial eigenvalue problems P ( λ ) x = 0 is to convert the matrix polynomial P ( λ ) into a matrix pencil that preserves its spectral information - a process known as linearization. When P ( λ ) is palindromic, the ei

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::50102cee3a364614f101b0cd701e22c4
https://doi.org/10.1016/j.cam.2011.09.010

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