scholarly journals Block Kronecker linearizations of matrix polynomials and their backward errors

2018 ◽  
Vol 140 (2) ◽  
pp. 373-426 ◽  
Author(s):  
Froilán M. Dopico ◽  
Piers W. Lawrence ◽  
Javier Pérez ◽  
Paul Van Dooren
Keyword(s):  
Matrix Polynomials ◽  
Backward Errors

scholarly journals Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations

2019 ◽  
Vol 89 (322) ◽  
pp. 767-805
Author(s):  
Luis Miguel Anguas ◽  
Maria Isabel Bueno ◽  
Froilán M. Dopico
Keyword(s):  
Möbius Transformations ◽  
Matrix Polynomials ◽  
Homogeneous Matrix ◽  
Backward Errors ◽  
Mobius Transformations

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].

scholarly journals A Schur-Cohn theorem for matrix polynomials

1990 ◽  
Vol 33 (3) ◽  
pp. 337-366 ◽  
Author(s):  
Harry Dym ◽  
Nicholas Young
Keyword(s):  
Unit Circle ◽  
Matrix Polynomial ◽  
Hermitian Matrix ◽  
Krein Space ◽  
Gram Matrix ◽  
Natural Basis ◽  
Test Matrix ◽  
Matrix Polynomials ◽  
Rational Vector ◽  
Square Matrix

Let N(λ) be a square matrix polynomial, and suppose det N is a polynomial of degree d. Subject to a certain non-singularity condition we construct a d by d Hermitian matrix whose signature determines the numbers of zeros of N inside and outside the unit circle. The result generalises a well known theorem of Schur and Cohn for scalar polynomials. The Hermitian “test matrix” is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with N. More complete results in a somewhat different formulation have been obtained by Lerer and Tismenetsky by other methods.

scholarly journals Structured backward errors for generalized saddle point systems

2012 ◽  
Vol 436 (9) ◽  
pp. 3109-3119 ◽  
Author(s):  
Xiao Shan Chen ◽  
Wen Li ◽  
Xiaojun Chen ◽  
Jun Liu
Keyword(s):  
Saddle Point ◽  
Backward Errors
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