S. Vologiannidis

A new family of companion forms of polynomial matrices

In this paper a new family of companion forms associated to a regular polynomial matrix is presented. Similar results have been presented in a recent paper by M. Fiedler, where the scalar case is considered. It is shown that the new family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen as linearizations of the corresponding polynomial matrix. Furthermore, for the special class of self-adjoint polynomial matrices a particular member is shown to be self-adjoint itself.

A permuted factors approach for the linearization of polynomial matrices

In Antoniou and Vologiannidis (Electron J Linear Algebra 11:78–87, 2004; 15:107–114, 2006), a new family of companion forms associated with a regular polynomial matrix T (s) has been presented, using products of permutations of n elementary matrices, generalizing similar results presented in Fiedler (Linear Algebra Its Appl 371:325–331, 2003) where the scalar case was considered. In this paper, extending this “permuted factors” approach, we present a broader family of companion-like linearizations, using products of up to n(n−1)/2 elementary matrices, where n is the degree of the polynomial matrix. Under given conditions, the proposed linearizations can be shown to consist of block entries where the coefficients of the polynomial matrix appear intact. Additionally, we provide a criterion for those linearizations to be block symmetric. We also illustrate several new block symmetric linearizations of the original polynomial matrix T (s), where in some of them the constraint of nonsingularity of the constant term and the coefficient of maximum degree are not a prerequisite.

Inverses of multivariable polynomial matrices by discrete fourier transforms

The problem of the fast computation of the Moore–Penrose and Drazin inverse of a multi-variable polynomial matrix is addressed. The algorithms proposed, use evaluation-interpolation techniques and the Fast Fourier transform. They proved to be faster than other known algorithms. The efficiency of the algorithms is illustrated via randomly generated examples.

A new notion of equivalence for discrete time AR representations

We present a new equivalence transformation termed divisor equivalence, that has the property of preserving both the finite and the infinite elementary divisor structures of a square non-singular polynomial matrix. This equivalence relation extends the known notion of strict equivalence, which dealt only with matrix pencils, to the general polynomial matrix case. It is proved that divisor equivalence characterizes in a closed form relation the equivalence classes of polynomial matrices that give rise to fundamentally equivalent discrete time auto-regressive representations.

WISE 2014 Challenge: Multi-label Classification of Print Media Articles to Topics

The WISE 2014 challenge was concerned with the task of multi-label classification of articles coming from Greek print media. Raw data comes from the scanning of print media, article segmentation, and optical character segmentation, and therefore is quite noisy. Each article is examined by a human annotator and categorized to one or more of the topics being monitored. Topics range from specific persons, products, and companies that can be easily categorized based on keywords, to more general semantic concepts, such as environment or economy. Building multi-label classifiers for the automated annotation of articles into topics can support the work of human annotators by suggesting a list of all topics by order of relevance, or even automate the annotation process for media and/or categories that are easier to predict. This saves valuable time and allows a media monitoring company to expand the portfolio of media being monitored. This paper summarizes the approaches of the top 4 among the 121 teams that participated in the competition.

Linearizations of Polynomial Matrices with Symmetries and Their Applications.

In E.N. Antoniou and S. Vologiannidis ( 2004), a new family of companion forms associated to a regular polynomial matrix has been presented generalizing similar results presented by M. Fiedler in M. Fiedler (2003) where the scalar case was considered. This family of companion forms preserves both the finite and infinite elementary divisors structure of the original polynomial matrix, thus all its members can be seen as linearizations of the corresponding polynomial matrix. In this note we examine its applications on polynomial matrices with symmetries which appear in a number of engineering fields

Zero coprime equivalent matrix pencils of a 2 - D polynomial matrix

In this paper we propose a procedure to reduce a 2 - D square polynomial matrix of arbitrary degrees to matrix pencils of the form sX + ZY + A, using zero coprime equivalence. As a further step, we provide the necessary and sufficient condition by which pencils of specific forms, appearing as parametric families, are zero coprime equivalent to a 2 - D regular polynomial matrix. Appropriate examples are provided to illustrate the use of proven results.

DFT calculation of the generalized and Drazin inverse of a polynomial matrix

A new algorithm is presented for the determination of the generalized inverse and the Drazin inverse of a polynomial matrix. The proposed algorithm is based on the discrete Fourier transform and thus is computationally fast in contrast to other known algorithms. The above algorithm is implemented in the Mathematica programming language and illustrated via examples.

NOTIONS OF EQUIVALENCE FOR DISCRETE TIME AR-REPRESENTATIONS

A transformation of polynomial matrices which preserves both the finite and infinite elementary divisor structure is presented and related to other known transformations.

On the characterization and parametrization of strong linearizations of polynomial matrices

In the present note, a new characterization of strong linearizations, corresponding to a given regular polynomial matrix, is presented. A linearization of a regular polynomial matrix is a matrix pencil which captures the finite spectral structure of the original matrix, while a strong linearization is one incorporating its structure at infinity along with the finite one. In this respect, linearizations serve as a tool for the study of spectral problems where polynomial matrices are involved. In view of their applications, many linearization techniques have been developed by several authors in the recent years. In this note, a unifying approach is proposed for the construction of strong linearizations aiming to serve as a bridge between approaches already known in the literature.