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Mathematics
Special Issues
Numerical Linear Algebra with Applications
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Numerical Linear Algebra with Applications

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 December 2016) | Viewed by 16597

Special Issue Editor

Prof. Dr. Khalide Jbilou

E-Mail Website
Guest Editor
1. Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral Côte d’Opale, BP 699-62228 Calais Cedex, France
2. Laboratory MSDA, University Polytechnic Mohammed VI, Benguerir 43150, Morocco
Interests: numerical linear algebra- matrix computation; control theory; model reduction; extrapolation methods; inverse, ill-posed problems and image restoration; numerical meshless methods for PDE's

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to some numerical linear algebra methods with applications to control, model reduction and ill-posed problems. The main topics of this Special Issue are:

  • Large linear and nonlinear systems of equations; Eigenvalues problems.
  • Preconditioning techniques
  • Ill-posed problems
  • Large scale matrix equation and applications to optimal control
  • Model reduction methods in large-scale dynamical systems
  • Linear algebra for image restoration

Accepted papers of this Special Issue should be original research papers or good survey papers that are not submitted for publication elsewhere. These papers will be accepted after a thorough peer-review.

Prof. Khalide Jbilou
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Numerical Linear Algebra
  • Systems of Linear Equations
  • Krylov Subspaces
  • Model Reduction
  • Large-Scale Matrix Equations
  • Ill Posed Problems

Published Papers (3 papers)

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Research

314 KiB  
Article
On Some Extended Block Krylov Based Methods for Large Scale Nonsymmetric Stein Matrix Equations
by Abdeslem Hafid Bentbib, Khalide Jbilou and EL Mostafa Sadek
Mathematics 2017, 5(2), 21; https://doi.org/10.3390/math5020021 - 27 Mar 2017
Cited by 7 | Viewed by 3668
Abstract
In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term A X B − X + E F T = 0 . These matrix equations appear in many applications in discrete-time control problems, filtering and image [...] Read more.
In the present paper, we consider the large scale Stein matrix equation with a low-rank constant term A X B − X + E F T = 0 . These matrix equations appear in many applications in discrete-time control problems, filtering and image restoration and others. The proposed methods are based on projection onto the extended block Krylov subspace with a Galerkin approach (GA) or with the minimization of the norm of the residual. We give some results on the residual and error norms and report some numerical experiments. Full article
(This article belongs to the Special Issue Numerical Linear Algebra with Applications)
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2259 KiB  
Article
Data Clustering with Quantum Mechanics
by Tony C. Scott, Madhusudan Therani and Xing M. Wang
Mathematics 2017, 5(1), 5; https://doi.org/10.3390/math5010005 - 06 Jan 2017
Cited by 9 | Viewed by 7511
Abstract
Data clustering is a vital tool for data analysis. This work shows that some existing useful methods in data clustering are actually based on quantum mechanics and can be assembled into a powerful and accurate data clustering method where the efficiency of computational [...] Read more.
Data clustering is a vital tool for data analysis. This work shows that some existing useful methods in data clustering are actually based on quantum mechanics and can be assembled into a powerful and accurate data clustering method where the efficiency of computational quantum chemistry eigenvalue methods is therefore applicable. These methods can be applied to scientific data, engineering data and even text. Full article
(This article belongs to the Special Issue Numerical Linear Algebra with Applications)
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702 KiB  
Article
Geometrical Inverse Preconditioning for Symmetric Positive Definite Matrices
by Jean-Paul Chehab and Marcos Raydan
Mathematics 2016, 4(3), 46; https://doi.org/10.3390/math4030046 - 09 Jul 2016
Cited by 2 | Viewed by 4244
Abstract
We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods [...] Read more.
We focus on inverse preconditioners based on minimizing F ( X ) = 1 − cos ( X A , I ) , where X A is the preconditioned matrix and A is symmetric and positive definite. We present and analyze gradient-type methods to minimize F ( X ) on a suitable compact set. For this, we use the geometrical properties of the non-polyhedral cone of symmetric and positive definite matrices, and also the special properties of F ( X ) on the feasible set. Preliminary and encouraging numerical results are also presented in which dense and sparse approximations are included. Full article
(This article belongs to the Special Issue Numerical Linear Algebra with Applications)
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