Parametrizing Structure Preserving Transformations of Matrix Polynomials

2012 ◽  
pp. 403-424 ◽  
Author(s):  
Peter Lancaster ◽  
Ion Zaballa
Keyword(s):  
Structure Preserving ◽  
Matrix Polynomials

scholarly journals Palindromic quadratization and structure-preserving algorithm for palindromic matrix polynomials of even degree

2011 ◽  
Vol 118 (4) ◽  
pp. 713-735 ◽  
Author(s):  
Tsung-Ming Huang ◽  
Wen-Wei Lin ◽  
Wei-Shuo Su
Keyword(s):  
Structure Preserving ◽  
Matrix Polynomials

scholarly journals Deflating quadratic matrix polynomials with structure preserving transformations

2011 ◽  
Vol 435 (3) ◽  
pp. 464-479 ◽  
Author(s):  
Françoise Tisseur ◽  
Seamus D. Garvey ◽  
Christopher Munro
Keyword(s):  
Structure Preserving ◽  
Matrix Polynomials ◽  
Quadratic Matrix

scholarly journals Parameterized Structure-Preserving Transformations of Matrix Polynomials

2020 ◽  
Vol 36 (36) ◽  
pp. 723-743
Author(s):  
Daniel T. Kawano
Keyword(s):  
Canonical Form ◽  
Equivalence Transformation ◽  
Regular Matrix ◽  
Quadratic Polynomials ◽  
Structure Preserving ◽  
Matrix Polynomials ◽  
The Relationship

This paper examines the relationship between the companion forms of regular matrix polynomials with singular leading coefficients. When two such polynomials have the same underlying finite and infinite Jordan structures, it is shown that their companion forms are connected by a strict equivalence transformation that can be parameterized using the commutant of the companion forms' common Weierstrass canonical form. The process developed herein for generating such parameterized transformations is applied to the useful class of diagonalizable quadratic polynomials.

scholarly journals Structured eigenvalue backward errors of matrix polynomials

2015 ◽  
Author(s):  
Punit Sharma ◽  
Shreemayee Bora ◽  
Michael Karow ◽  
Christian Mehl
Keyword(s):  
Numerical Results ◽  
Real Matrix ◽  
Structure Preserving ◽  
Matrix Polynomials ◽  
Significant Difference ◽  
Matrix Pencils ◽  
Backward Errors

In this poster, we briefly present some results on eigenvalue backward errors of matrix pencils and polynomials under structure preserving perturbations. We also present eigenvalue backward errors of real matrix pencils with respect to real perturbations that also preserve certain structures like symmetric, T-alternating and T-palindromic. Numerical results show that there is a significant difference between the backward errors with respect to perturbations that preserve structures and those with respect to arbitrary perturbations.

A general inverse matrix series relation and associated polynomials – II

2021 ◽  
Vol 71 (2) ◽  
pp. 301-316
Author(s):  
Reshma Sanjhira
Keyword(s):  
Matrix Polynomial ◽  
Combinatorial Identities ◽  
Inverse Matrix ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Series Representations ◽  
The Matrix ◽  
Associated Polynomials ◽  
Matrix Pair ◽  
Matrix Series

Abstract We propose a matrix analogue of a general inverse series relation with an objective to introduce the generalized Humbert matrix polynomial, Wilson matrix polynomial, and the Rach matrix polynomial together with their inverse series representations. The matrix polynomials of Kiney, Pincherle, Gegenbauer, Hahn, Meixner-Pollaczek etc. occur as the special cases. It is also shown that the general inverse matrix pair provides the extension to several inverse pairs due to John Riordan [An Introduction to Combinatorial Identities, Wiley, 1968].

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