Linearization of matrix polynomials expressed in polynomial bases

By Amirhossein Amiraslani, Robert M Corless, Peter Lancaster. 2008

127 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/70d410504ac39b6238c40a9217b4a9f30a503dfb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Spectral equivalence of matrix polynomials and the index sum theorem (2014, methodology): “Alternative definitions for linearizations and strong linearizations of regular polynomials have been given in [30], and then used extensively in [1].”
Möbius transformations of matrix polynomials (2015, methodology): “This extension was used in [3] to study linearizations.”
LINEARIZATIONS OF SINGULAR MATRIX POLYNOMIALS AND THE RECOVERY OF MINIMAL INDICES (2009, methodology): “All of the new classes of linearizations introduced in [2, 4, 25] have been studied only for regular matrix polynomials.”
Fiedler companion linearizations for rectangular matrix polynomials (2012, background): “At first, only linearizations for regular matrix polynomials were considered [1, 2, 23, 27, 28], while more recently square singular polynomials have also received attention [10, 11, 12, 34].”
Chebyshev interpolation for nonlinear eigenvalue problems (2012, methodology): “For the sake of completeness, let us recall the linearization technique from [1] for the polynomial eigenvalue problem ( P0τ0(λ) + · · · + Pdτd(λ) ) x = 0 (2.”
A framework for analyzing nonlinear eigenproblems and parametrized linear systems (2011, background): “[2] construct pencils L(λ) = λX + Y that are defined in terms of the Bi and the coefficients of the recurrence and are linearizations of P.”
Linearization of regular matrix polynomials (2008, methodology): “and P (λ )i sregular ,i . e. det P (λ) does not vanish identically.The main ideas to be developed first appeared in the paper [6] but seem to have been largely overlooked by the linear algebra community.In large measure, therefore, this exposition repeats what has been developed more succinctly in [”
Linear Algebra and its Applications (2010, unknown): “Typically, j v represents the given source current J E , but j u and j v may also contain boundary data.”