# Mustapha HachedUniversité de Lille · Institut Universitaire de Technologie (IUT"A")

Mustapha Hached

PhD

## About

18

Publications

2,612

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126

Citations

Citations since 2017

Introduction

Mustapha Hached currently works at the Département de Chimie, IUT A, Université des Sciences et Technologies de Lille 1. Mustapha does research in Applied Mathematics, mainly in numerical linear algebra. Their most recent publication is 'Numerical methods for differential linear matrix equations via Krylov subspace methods'.

Additional affiliations

September 2013 - present

September 2013 - present

September 2008 - present

**Université des Sciences et Technologies de Lille 1, France**

Position

- Lecturer (mathematics), International relations officer

## Publications

Publications (18)

Face recognition and identification are very important applications in machine learning. Due to the increasing amount of available data, traditional approaches based on matricization and matrix PCA methods can be difficult to implement. Moreover, the tensorial approaches are a natural choice, due to the mere structure of the databases, for example...

Face recognition and identification is a very important application in machine learning. Due to the increasing amount of available data, traditional approaches based on matricization and matrix PCA methods can be difficult to implement. Moreover, the tensorial approaches are a natural choice, due to the mere structure of the databases, for example...

Nonsymmetric differential matrix Riccati equations arise in many problems related to science and engineering. This work is focusing on the sensitivity of the solution to perturbations in the matrix coefficients and the initial condition. Two approaches of nonlocal perturbation analysis of the symmetric differential Riccati equation are extended to...

In the present paper, we present some numerical methods for computing approximate solutions to some large differential linear matrix equations. In the first part of this work, we deal with differential generalized Sylvester matrix equations with full rank right-hand sides using a global Galerkin and a norm-minimization approaches. In the second par...

In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations. The first approach is based on the integral expression of the exact solution and an approximation method for the computation of the ex...

In the present paper, we present some numerical methods for computing approximate solutions to some large differential linear matrix equations. In the first part of this work, we deal with differential generalized Sylvester matrix equations with full rank right-hand sides using a global Galerkin and a norm-minimization approaches. In the second par...

In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability and others. We show how to apply Krylov-type methods such as the extended block Arnoldi algorithm to get low...

In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first approach is based on the integral expression of the exact solution and a Krylov method for the computation of t...

In this paper, we propose two new approaches for model order reduction of large-scale multi-input multi-output (MIMO) linear time invariant dynamical systems (LTI). These methods are based on a generalization of the global Arnoldi algorithm which is used to generate projection subspaces. An adaptive procedure for the selection of shift parameters i...

In the present paper, we consider large-scale continuous-time differential matrix Riccati equations having low rank right-hand sides. These equations are generally solved by Backward Differentiation Formula (BDF) or Rosenbrock methods leading to a large scale algebraic Riccati equation which has to be solved for each timestep. We propose a new appr...

In recent years, a great interest has been shown towards Krylov subspace techniques applied to model order reduction of large-scale dynamical systems. A special interest has been devoted to single-input single-output (SISO) systems by using moment matching techniques based on Arnoldi or Lanczos algorithms. In this paper, we consider multiple-input...

In the present paper, we propose a preconditioned Newton-Block Arnoldi method for solving large continuous time algebraic Riccati equations. Such equations appear in control theory, model reduction, circuit simulation amongst other problems. At each step of the Newton process, we solve a large Lyapunov matrix equation with a low rank right hand sid...

In this paper, we introduce a modernized and improved version of the Davison-Man method for the numerical resolution of Sylvester matrix equations. In the case of moderate size problems, we give some background facts about this iterative method, addressing the problem of stagnation and we propose an iterative refinement technique to improve its acc...

In this paper, we discuss a meshless method for the computation of a numerical solution of unsteady coupled Burgers’-type equations which are, in the most general case, nonlinear partial differential equations. Our approach is based on the interpolation of the solution by radial basis functions (RBFs) and is independent of the geometry of the domai...

In this paper, we discuss a meshless method for solving steady Burgers-type equations with Dirichlet boundary conditions. The numerical approximation of the solution in the given domain is obtained by using thin plate spline approximation, leading to a large-scale nonlinear matrix equation. The main difficulty of the proposed method is the numerica...

In this paper, we propose a block Arnoldi method for solving the continuous low-rank Sylvester matrix equation AX + XB = EFT. We consider the case where both A and B are large and sparse real matrices, and E and F are real matrices with small rank. We first apply an alternating directional implicit preconditioner to our equation, turning it into a...

This thesis deals with some matrix equations involved in numerical resolution of partial differential equations and linear control. We first consider some numerical resolution techniques of linear matrix equation. In the second part of this thesis, we apply these resolution techniques to problems related to partial differential equations.

## Projects

Project (1)