Infinite invertible arrowhead matrices and applications

Motivated by current applications of the arrowhead matrices of large order, the infinite invertible arrowhead matrices are considered. A method based on a simple but suitable triangular factorization is proposed for obtaining, in the finite-dimensional case, a decomposition of the inverse in O(n) time. This procedure can be applicable to infinite arrowhead matrices factored properly. Some illustrative examples are given

LINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS IN ARROWHEAD FORM

This paper deals with different approaches for solving linear systems of the first order differential equations with the system matrix in the symmetric arrowhead form.Some needed algebraic properties of the symmetric arrowhead matrix are proposed.We investigate the form of invariant factors of the arrowhead matrix.Also the entries of the adjugate matrix of the characteristic matrix of the arrowhead matrix are considered. Some reductions techniques for linear systems of differential equations with the system matrix in the arrowhead form are presented

Perturbation bounds on the extremal singular values of a matrix after appending a column

In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal processing, control theory and many other fields. In the first part of this paper, we review and compare various bounds from recent research papers on this subject. We also present a new lower bound and a new upper bound on the perturbation of the operator norm is provided. Simple proofs are provided, based on the study of the characteristic polynomial rather than on variational methods, as e.g. in \cite{Li-Li}. In a second part of the paper, we present applications to signal processing and control theory

Innovative sparse representation algorithms for robust face recognition

In this paper, we propose two innovative and computationally efficient algorithms for robust face recognition, which extend the previous Sparse Representation-based Classification (SRC) algorithm proposed by Wright et al. (2009). The two new algorithms, which are designed for both batch and online modes, operate on matrix representation of images, as opposed to vector representation in SRC, to achieve efficiency whilst maintaining the recognition performance. We first show that, by introducing a matrix representation of images, the size of the ℓ1-norm problem in SRC is reduced fromO(whN) to O(rN), where r ≪ wh and thus higher computational efficiency can be obtained. We then show that the computational efficiency can be even enhanced with an online setting where the training images arrive incrementally by exploiting the interlacing property of eigenvalues in the inner product matrix. Finally, we demonstrate the superior computational efficiency and robust performance of the proposed algorithms in both batch and online modes, as compared with the original SRC algorithm through numerous experimental studies

Hardware-software design of embedded systems for intelligent sensing applications

This Thesis wants to highlight the importance of ad-hoc designed and developed embedded systems in the implementation of intelligent sensor networks. As evidence four areas of application are presented: Precision Agriculture, Bioengineering, Automotive and Structural Health Monitoring. For each field is reported one, or more, smart device design and developing, in addition to on-board elaborations, experimental validation and in field tests. In particular, it is presented the design and development of a fruit meter. In the bioengineering field, three different projects are reported, detailing the architectures implemented and the validation tests conducted. Two prototype realizations of an inner temperature measurement system in electric motors for an automotive application are then discussed. Lastly, the HW/SW design of a Smart Sensor Network is analyzed: the network features on-board data management and processing, integration in an IoT toolchain, Wireless Sensor Network developments and an AI framework for vibration-based structural assessment

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum