**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**12

# Linear Systems Related Publications

##### 12 Number of Parametrization of Discrete-Time Systems without Unit-Delay Element: Single-Input Single-Output Case

**Authors:**
Kazuyoshi Mori

**Abstract:**

**Keywords:**
Linear Systems,
parametrization,
number of parameters,
Coprime
Factorization

##### 11 3-D Visualization and Optimization for SISO Linear Systems Using Parametrization of Two-Stage Compensator Design

**Authors:**
Kazuyoshi Mori,
Keisuke Hashimoto

**Abstract:**

**Keywords:**
Linear Systems,
Optimization,
Visualization,
Mathematica,
two-Stage
compensator design

##### 10 Calculus Logarithmic Function for Image Encryption

**Authors:**
Adil Al-Rammahi

**Abstract:**

When we prefer to make the data secure from various attacks and fore integrity of data, we must encrypt the data before it is transmitted or stored. This paper introduces a new effective and lossless image encryption algorithm using a natural logarithmic function. The new algorithm encrypts an image through a three stage process. In the first stage, a reference natural logarithmic function is generated as the foundation for the encryption image. The image numeral matrix is then analyzed to five integer numbers, and then the numbers’ positions are transformed to matrices. The advantages of this method is useful for efficiently encrypting a variety of digital images, such as binary images, gray images, and RGB images without any quality loss. The principles of the presented scheme could be applied to provide complexity and then security for a variety of data systems such as image and others.

**Keywords:**
Linear Systems,
Calculus,
Image Encryption

##### 9 Power Series Form for Solving Linear Fredholm Integral Equations of Second Order via Banach Fixed Point Theorem

**Authors:**
Adil Al-Rammahi

**Abstract:**

In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.

**Keywords:**
Linear Systems,
Fredholm Integral Equation,
Banach fixed point theorem,
power series

##### 8 Multi-Rate Exact Discretization based on Diagonalization of a Linear System - A Multiple-Real-Eigenvalue Case

**Authors:**
T. Sakamoto,
N. Hori

**Abstract:**

**Keywords:**
Linear Systems,
similarity transformation,
Multi-rate discretization,
triangularization,
diagonalization,
exponential transformation,
multiple eigenvalues

##### 7 Note to the Global GMRES for Solving the Matrix Equation AXB = F

**Authors:**
Fatemeh Panjeh Ali Beik

**Abstract:**

In the present work, we propose a new projection method for solving the matrix equation AXB = F. For implementing our new method, generalized forms of block Krylov subspace and global Arnoldi process are presented. The new method can be considered as an extended form of the well-known global generalized minimum residual (Gl-GMRES) method for solving multiple linear systems and it will be called as the extended Gl-GMRES (EGl- GMRES). Some new theoretical results have been established for proposed method by employing Schur complement. Finally, some numerical results are given to illustrate the efficiency of our new method.

**Keywords:**
Linear Systems,
Iterative Method,
Matrix Equation,
block Krylov subspace method,
global generalized minimum residual (Gl-GMRES)

##### 6 Optimal Control of a Linear Distributed Parameter System via Shifted Legendre Polynomials

**Authors:**
Sanjeeb Kumar Kar

**Abstract:**

**Keywords:**
Linear Systems,
Optimal Control,
distributed parametersystems,
Legendre polynomials

##### 5 Parallel Multisplitting Methods for Singular Linear Systems

**Authors:**
Guangbin Wang,
Fuping Tan

**Abstract:**

In this paper, we discuss convergence of the extrapolated iterative methods for linear systems with the coefficient matrices are singular H-matrices. And we present the sufficient and necessary conditions for convergence of the extrapolated iterative methods. Moreover, we apply the results to the GMAOR methods. Finally, we give one numerical example.

**Keywords:**
Linear Systems,
Convergence,
Singular H-matrix,
extrapolated iterative method,
GMAOR method

##### 4 The Approximate Solution of Linear Fuzzy Fredholm Integral Equations of the Second Kind by Using Iterative Interpolation

**Authors:**
N. Parandin,
M. A. Fariborzi Araghi

**Abstract:**

**Keywords:**
Linear Systems,
Iterative Method,
Fuzzy function integral equations,
Parametric form of fuzzy number

##### 3 Combining Minimum Energy and Minimum Direct Jerk of Linear Dynamic Systems

**Authors:**
V. Tawiwat,
P. Jumnong

**Abstract:**

**Keywords:**
Linear Systems,
Optimization,
Dynamic,
Jerks

##### 2 Analysis and Application of in Indirect MinimumJerk Method for Higher order Differential Equation in Dynamics Optimization Systems

**Authors:**
V. Tawiwat,
T. Amornthep,
P. Pnop

**Abstract:**

**Keywords:**
Linear Systems,
Optimization,
Dynamic,
Jerks

##### 1 Comparison between Minimum Direct and Indirect Jerks of Linear Dynamic Systems

**Authors:**
Tawiwat Veeraklaew,
Nathasit Phathana-im,
Songkit Heama

**Abstract:**

**Keywords:**
Linear Systems,
Optimization,
Dynamic,
Jerks