Journal of Mathematics

Linear and Nonlinear Matrix Equations: Solutions, Convergence, Perturbation, and Optimization

Publishing date
01 May 2022
Submission deadline
17 Dec 2021

1Vellore Institute of Technology, Vellore, India

2Shumen University, Shumen, Bulgaria

3Institute for Advanced Studies in Basic Sciences, Zanjan, Iran

This issue is now closed for submissions.

Linear and Nonlinear Matrix Equations: Solutions, Convergence, Perturbation, and Optimization

This issue is now closed for submissions.


The study of numerical methods for linear and nonlinear algebraic systems arises when modeling many different problems in applied science. To be more precise, the study of nonlinear matrix equations (NMEs) first arose in the literature with algebraic Riccati equations and plays a central role in several engineering and mathematical models. NMEs have great importance in infinite-horizon optimal control problems in continuous-time or discrete-time formats.

As such, they have been studied extensively in recent decades, producing a vast literature with applications in control theory, dynamical programming, ladder networks, queueing theory, and statistics, among others. Over the years, many authors have studied these types of matrix equations to compute their positive definite solutions (PDS) using different iterative methods, allowing them to identify the solution. Researchers have introduced algorithms for obtaining the PDS of some matrix equations, some of which use the basic fixed point iterative method and its accelerated version, while others use the inversion-free method, two-sided iterative method, Newton's method, monotone Newton-like method, or perturbation bounds of positive solution.

This Special Issue is devoted to publishing modern and noteworthy research on linear and nonlinear matrix equations and all their characteristics. Our objectives are to highlight the latest progress and developments on the theory, techniques, and results of linear and nonlinear matrix equations.

Potential topics include but are not limited to the following:

  • Iterative solutions of matrix equations
  • Positive definite solutions of matrix equations
  • Closed-form solutions and solvability of matrix equations
  • Perturbation analysis of matrix equations
  • Algebraic matrix equations
  • Differential matrix equations
  • Numerical algorithms
  • Iterative methods with and without memory
  • Applications of fixed-point theorems to matrix equations
  • Generalized inverses and fast algorithms for matrix functions
  • Iterative methods for inverse problems
  • Matrix equations with applications to control theory
  • Matrix inequalities
  • Matrix methods in partial differential equations (PDEs)


  • Special Issue
  • - Volume 2022
  • - Article ID 9621026
  • - Research Article

Functional Approach for Solving Reduced Order of Index-Four Hessenberg Differential-Algebraic Control System

Ghazwa F. Abd
  • Special Issue
  • - Volume 2021
  • - Article ID 8862139
  • - Research Article

Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines

Arshad Hussain | Marjan Uddin | ... | Hameed Ullah Jan
  • Special Issue
  • - Volume 2021
  • - Article ID 2123897
  • - Research Article

A Study on the Convergence Analysis of the Inexact Simplified Jacobi–Davidson Method

Jutao Zhao | Pengfei Guo
  • Special Issue
  • - Volume 2021
  • - Article ID 2046726
  • - Research Article

Some Results on the Extended Hypergeometric Matrix Functions and Related Functions

Mohamed Abdalla | Sahar Ahmed Idris | Ibrahim Mekawy
  • Special Issue
  • - Volume 2021
  • - Article ID 4064508
  • - Research Article

Energy of Nonsingular Graphs: Improving Lower Bounds

Hajar Shooshtari | Jonnathan Rodriguez | ... | Abbas Shokri
  • Special Issue
  • - Volume 2021
  • - Article ID 2667885
  • - Research Article

Latest Inversion-Free Iterative Scheme for Solving a Pair of Nonlinear Matrix Equations

Sourav Shil | Hemant Kumar Nashine
  • Special Issue
  • - Volume 2021
  • - Article ID 4612177
  • - Research Article

On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation

Yunbo Tian | Chao Xia
Journal of Mathematics
 Journal metrics
See full report
Acceptance rate14%
Submission to final decision111 days
Acceptance to publication25 days
Journal Citation Indicator1.140
Impact Factor1.4
 Submit Check your manuscript for errors before submitting

Article of the Year Award: Impactful research contributions of 2022, as selected by our Chief Editors. Discover the winning articles.