Fiedler Companion Linearizations and the Recovery of Minimal Indices

@article{Tern2010FiedlerCL,
  title={Fiedler Companion Linearizations and the Recovery of Minimal Indices},
  author={F. Ter{\'a}n and F. Dopico and D. S. Mackey},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2010},
  volume={31},
  pages={2181-2204}
}
A standard way of dealing with a matrix polynomial $P(\lambda)$ is to convert it into an equivalent matrix pencil—a process known as linearization. For any regular matrix polynomial, a new family of linearizations generalizing the classical first and second Frobenius companion forms has recently been introduced by Antoniou and Vologiannidis, extending some linearizations previously defined by Fiedler for scalar polynomials. We prove that these pencils are linearizations even when $P(\lambda… Expand
94 Citations
Fiedler companion linearizations for rectangular matrix polynomials
  • 47
  • PDF
Structured Linearizations for Palindromic Matrix Polynomials of Odd Degree
  • 9
  • PDF
Palindromic companion forms for matrix polynomials of odd degree
  • 35
  • PDF
Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis
  • PDF
A permuted factors approach for the linearization of polynomial matrices
  • 54
  • Highly Influenced
  • PDF
Block minimal bases $\ell$-ifications of matrix polynomials
  • 10
  • Highly Influenced
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 43 REFERENCES
Symmetric Linearizations for Matrix Polynomials
  • 125
  • PDF
The Conditioning of Linearizations of Matrix Polynomials
  • 120
  • PDF
Vector Spaces of Linearizations for Matrix Polynomials
  • 292
  • PDF
Structured Linearizations for Matrix Polynomials
  • 22
  • PDF
A Note on Weak and Strong Linearizations of Regular Matrix Polynomials
  • 41
  • PDF
Definite Matrix Polynomials and their Linearization by Definite Pencils
  • 35
  • PDF
Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
  • 708
...
1
2
3
4
5
...