A. Nazari

[ 1 ] - Computational aspect to the nearest southeast submatrix that makes multiple a prescribed eigenvalue

Given four complex matrices $A$‎, ‎$B$‎, ‎$C$ and $D$ where $Ainmathbb{C}^{ntimes n}$‎ ‎and $Dinmathbb{C}^{mtimes m}$ and let the matrix $left(begin{array}{cc}‎ A & B ‎ C & D‎ end{array} right)$ be a normal matrix and‎ assume that $lambda$ is a given complex number‎ ‎that is not eigenvalue of matrix $A$‎. ‎We present a method to calculate the distance norm (with respect to 2-norm) from $D$‎ to ...

[ 2 ] - Steffensen method for solving nonlinear matrix equation $X+A^T X^{(-1)}A=Q$

In this article we study Steffensen method to solve nonlinear matrix equation $X+A^T X^{(-1)}A=Q$, when $A$ is a normal matrix. We establish some conditions that generate a sequence of positive denite matrices which converges to solution of this equation.

[ 3 ] - On the construction of symmetric nonnegative matrix with prescribed Ritz values

In this paper for a given prescribed Ritz values that satisfy in the some special conditions, we find a symmetric nonnegative matrix, such that the given set be its Ritz values.

[ 4 ] - On the nonnegative inverse eigenvalue problem of traditional matrices

In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.

[ 5 ] - On the solving matrix equations by using the spectral representation

‎The purpose of this paper is to solve two types of Lyapunov equations and quadratic matrix equations by using the spectral representation‎. ‎We focus on solving Lyapunov equations $AX+XA^*=C$ and $AX+XA^{T}=-bb^{T}$ for $A‎, ‎X in mathbb{C}^{n times n}$ and $b in mathbb{C} ^{n times s}$ with $s < n$‎, ‎which $X$ is unknown matrix‎. ‎Also‎, ‎we suggest the new method for solving quadratic matri...

[ 6 ] - On the Remarkable Formula for Spectral Distance of Block Southeast Submatrix

‎‎‎This paper presents a remarkable formula for spectral distance of a given block normal matrix $G_{D_0} = begin{pmatrix}‎ ‎A & B \‎ ‎C & D_0‎ ‎end{pmatrix} $ to set of block normal matrix $G_{D}$ (as same as $G_{D_0}$ except block $D$ which is replaced by block $D_0$)‎, ‎in which $A in mathbb{C}^{ntimes n}$ is invertible‎, ‎$ B in mathbb{C}^{ntimes m}‎, ‎C in mathbb{C}^{mti...