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pro vyhledávání: '"van Dooren, Paul"'
In this paper we study para-Hermitian rational matrices and the associated structured rational eigenvalue problem (REP). Para-Hermitian rational matrices are square rational matrices that are Hermitian for all $z$ on the unit circle that are not pole
Externí odkaz:
http://arxiv.org/abs/2407.13563
Publikováno v:
J. Comput. Appl. Math. 451 (2024), 116109
The aim of this paper is to describe a Matlab package for computing the simultaneous Gaussian quadrature rules associated with a variety of multiple orthogonal polynomials. Multiple orthogonal polynomials can be considered as a generalization of clas
Externí odkaz:
http://arxiv.org/abs/2406.11269
Autor:
Gillis, Nicolas, Van Dooren, Paul
The target stationary distribution problem (TSDP) is the following: given an irreducible stochastic matrix $G$ and a target stationary distribution $\hat \mu$, construct a minimum norm perturbation, $\Delta$, such that $\hat G = G+\Delta$ is also sto
Externí odkaz:
http://arxiv.org/abs/2312.16011
We investigate rank revealing factorizations of $m \times n$ polynomial matrices $P(\lambda)$ into products of three, $P(\lambda) = L(\lambda) E(\lambda) R(\lambda)$, or two, $P(\lambda) = L(\lambda) R(\lambda)$, polynomial matrices. Among all possib
Externí odkaz:
http://arxiv.org/abs/2312.00676
We study the tangential interpolation problem for a passive transfer function in standard state-space form. We derive new interpolation conditions based on the computation of a deflating subspace associated with a selection of spectral zeros of a par
Externí odkaz:
http://arxiv.org/abs/2308.03500
Autor:
Noferini, Vanni, Van Dooren, Paul
We define a compact local Smith-McMillan form of a rational matrix $R(\lambda)$ as the diagonal matrix whose diagonal elements are the nonzero entries of a local Smith-McMillan form of $R(\lambda)$. We show that a recursive rank search procedure, app
Externí odkaz:
http://arxiv.org/abs/2303.10403
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 some of the
Externí odkaz:
http://arxiv.org/abs/2211.09056
Autor:
Noferini, Vanni, Van Dooren, Paul
In this paper we revisit the greatest common right divisor (GCRD) extraction from a set of polynomial matrices $P_i(\lambda)\in \F[\la]^{m_i\times n}$, $i=1,\ldots,k$ with coefficients in a generic field $\F$, and with common column dimension $n$. We
Externí odkaz:
http://arxiv.org/abs/2210.16234
This paper considers the optimization problem in the form of $\min_{X \in \mathcal{F}_v} f(x) + \lambda \|X\|_1,$ where $f$ is smooth, $\mathcal{F}_v = \{X \in \mathbb{R}^{n \times q} : X^T X = I_q, v \in \mathrm{span}(X)\}$, and $v$ is a given posit
Externí odkaz:
http://arxiv.org/abs/2208.03858
Autor:
Noferini, Vanni, Van Dooren, Paul
The notion of root polynomials of a polynomial matrix $P(\lambda)$ was thoroughly studied in [F. Dopico and V. Noferini, Root polynomials and their role in the theory of matrix polynomials, Linear Algebra Appl. 584:37--78, 2020]. In this paper, we ex
Externí odkaz:
http://arxiv.org/abs/2204.10955