arXiv subjects

E. Kokabifar

Publications and source records attributed to E. Kokabifar.

5 recordsLinked to original sources

arXiv2025

Prescribed Eigenvalues via Optimal Perturbation of main-diagonal submatrix

Consider a given square matrix $\textrm {K}$ with square blocks $A_{11},A_{22},\ldots,A_{nn}$ on the main diagonal. This paper aims to compute an optimal perturbation $Δ$ of a preassigned block $A_{ii}\in\mathbb{C}^{d_i\times d_k}, \left(1\le i\le n\right)$,with respect to the spectral norm distance, such that the perturbed matrix ${\textrm {K}_X}$ has $k \le d_i$ prescribed eigenvalues. This paper presents a method for constructing the optimal perturbation by improving and extending the methodology, necessary definitions and lemmas of previous related works. Some conceivable applications of this subject are also presented. Numerical experiments are provided to illustrate the validity of the method.

math.NA↗

arXiv2015

On the distance from a matrix polynomial to matrix polynomials with $k$ prescribed distinct eigenvalues

Consider an $n\times n$ matrix polynomial $P(λ)$ and a set $Σ$ consisting of $k \le n$ distinct complex numbers. In this paper, a (weighted) spectral norm distance from $P(λ)$ to the matrix polynomials whose spectra include the specified set $Σ$, is defined and studied. An upper and a lower bounds for this distance are obtained, and an optimal perturbation of $P(λ)$ associated to the upper bound is constructed. Numerical examples are given to illustrate the efficiency of the proposed bounds.

math.NA↗

arXiv2015

Digital image watermarking using normal matrices

This paper presents techniques for digital image watermarking based on eigenvalue decomposition of normal matrices. The introduced methods are convenient and self-explanatory, achieve satisfactory results, as well as require less and easy computations compared to some current methods. Through the proposed methods, host images and watermarks are transformed to the space of normal matrices, and the properties of spectral decompositions are dealt with to obtain watermarked images. Watermark extraction is carried out via a procedure similar to embedding. Experimental results are provided to illustrate the reliability and robustness of the methods.

math.NA↗

arXiv2015

A new approach for image compression using normal matrices

In this paper, we present methods for image compression on the basis of eigenvalue decomposition of normal matrices. The proposed methods are convenient and self-explanatory, requiring fewer and easier computations as compared to some existing methods. Through the proposed techniques, the image is transformed to the space of normal matrices. Then, the properties of spectral decomposition are dealt with to obtain compressed images. Experimental results are provided to illustrate the validity of the methods.

cs.MM↗

arXiv2014

On the distance from a weakly normal matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue

Consider an $n \times n$ matrix polynomial $P(λ)$. An upper bound for a spectral norm distance from $P(λ)$ to the set of $n \times n$ matrix polynomials that have a given scalar $μ\in\mathbb{C}$ as a multiple eigenvalue was recently obtained by Papathanasiou and Psarrakos (2008). This paper concerns a refinement of this result for the case of weakly normal matrix polynomials. A modification method is implemented and its efficiency is verified by an illustrative example.

math.NA↗