相关论文: Unified framework for Fiedler-like strong lineariz…
The standard way of solving the polynomial eigenvalue problem associated with a matrix polynomial is to embed the matrix polynomial into a matrix pencil, transforming the problem into an equivalent generalized eigenvalue problem. Such…
In the last decade, there has been a continued effort to produce families of strong linearizations of a matrix polynomial $P(\lambda)$, regular and singular, with good properties. As a consequence of this research, families such as the…
Numerical computations involving rational matrices often benefit from preserving underlying matrix structures such as symmetry, Hermitian properties, or sparsity that reflect physical, geometric, or algebraic characteristics of the system.…
Linearization is a standard method in the computation of eigenvalues and eigenvectors of matrix polynomials. In the last decade a variety of linearization methods have been developed in order to deal with algebraic structures and in order…
A well known method to solve the Polynomial Eigenvalue Problem (PEP) is via linearization. That is, transforming the PEP into a generalized linear eigenvalue problem with the same spectral information and solving such linear problem with…
Many applications give rise to structured matrix polynomials. The problem of constructing structure-preserving strong linearizations of structured matrix polynomials is revisited in this work and in the forthcoming ones…
Our aim in this paper is two-fold: First, for computing zeros of a linear time-invariant (LTI) system $\Sigma$ in {\em state-space form}, we introduce a "trimmed structured linearization", which we refer to as {\em Rosenbrock…
Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important source of linearizations are the so called Fiedler…
Structured rational matrices such as symmetric, skew-symmetric, Hamiltonian, skew-Hamiltonian, Hermitian, and para-Hermitian rational matrices arise in many applications. Linearizations of rational matrices have been introduced recently for…
The aim of this paper is twofold. First, we introduce a new class of linearizations, based on the generalization of a construction used in polynomial algebra to find the zeros of a system of (scalar) polynomial equations. We show that one…
We introduce a new family of strong linearizations of matrix polynomials---which we call "block Kronecker pencils"---and perform a backward stability analysis of complete polynomial eigenproblems. These problems are solved by applying any…
We construct a new family of strong linearizations of rational matrices considering the polynomial part of them expressed in a basis that satisfies a three term recurrence relation. For this purpose, we combine the theory developed by…
The seminal work by Mackey et al. in 2006 (reference [21] of the article) introduced vector spaces of matrix pencils, with the property that almost all the pencils in the spaces are strong linearizations of a given square regular matrix…
The standard way of solving a polynomial eigenvalue problem associated with a matrix polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil, known as a strong linearization. This process transforms the…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
In this paper, we introduce a new family of equations for matrix pencils that may be utilized for the construction of strong linearizations for any square or rectangluar matrix polynomial. We provide a comprehensive characterization of the…
One useful standard method to compute eigenvalues of matrix polynomials ${\bf P}(z) \in \mathbb{C}^{n\times n}[z]$ of degree at most $\ell$ in $z$ (denoted of grade $\ell$, for short) is to first transform ${\bf P}(z)$ to an equivalent…
We present a framework for the construction of linearizations for scalar and matrix polynomials based on dual bases which, in the case of orthogonal polynomials, can be described by the associated recurrence relations. The framework…
Message passing Graph Neural Networks (GNNs) are known to be limited in expressive power by the 1-WL color-refinement test for graph isomorphism. Other more expressive models either are computationally expensive or need preprocessing to…
In the framework of Polynomial Eigenvalue Problems, most of the matrix polynomials arising in applications are structured polynomials (namely (skew-)symmetric, (skew-)Hermitian, (anti-)palindromic, or alternating). The standard way to solve…