A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error

MI Bueno, FM Dopico, S Furtado, L Medina - Calcolo, 2018 - Springer
The standard way of solving numerically a polynomial eigenvalue problem (PEP) is to use a
linearization and solve the corresponding generalized eigenvalue problem (GEP). In …

Structured strong -ifications for structured matrix polynomials in the monomial basis

F De Terán, C Hernando, J Pérez - arXiv preprint arXiv:2010.06033, 2020 - arxiv.org
In the framework of Polynomial Eigenvalue Problems, most of the matrix polynomials arising
in applications are structured polynomials (namely (skew-) symmetric,(skew-) Hermitian,(anti …

[HTML][HTML] Automatic recovery of eigenvectors and minimal bases of matrix polynomials from generalized Fiedler pencils with repetition

RK Das, R Alam - Linear Algebra and its Applications, 2019 - Elsevier
Linearization is a widely used method for solving polynomial eigenproblems in which a
matrix polynomial is transformed to a matrix pencil of larger size. Fiedler pencils …

On why using for the symmetric polynomial eigenvalue problem might need to be reconsidered

MI Bueno, J Pérez, S Rogers - Calcolo, 2022 - Springer
In the literature it is common to use the first and last pencils D 1 (λ, P) and D k (λ, P) in the
“standard basis” for the vector space DL (P) of block-symmetric pencils to solve the …

[HTML][HTML] Generalized companion forms for scalar and matrix polynomials

CH Fuster - 2020 - dialnet.unirioja.es
Matrix polynomials arise frequently associated with Polynomial Eigenvalue Problems
(PEPs). The standard way to solve PEPs is by means of (strong) linearizations, which are …