**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**25

# Search results for: Matrix equation

##### 25 Conjugate Gradient Algorithm for the Symmetric Arrowhead Solution of Matrix Equation AXB=C

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

*AXB=C*and the associate optimal approximation problem are considered for the symmetric arrowhead matrix solutions in the premise of consistency. The convergence results of the method are presented. At last, a numerical example is given to illustrate the efficiency of this method.

**Keywords:**
Iterative Method,
Conjugate Gradient algorithm,
Symmetric arrowhead matrix

##### 24 The BGMRES Method for Generalized Sylvester Matrix Equation AXB − X = C and Preconditioning

**Authors:**
Azita Tajaddini,
Ramleh Shamsi

**Abstract:**

**Keywords:**
Linear matrix equation,
Block GMRES,
matrix Krylov
subspace,
polynomial preconditioner

##### 23 Frequency Transformation with Pascal Matrix Equations

**Authors:**
Phuoc Si Nguyen

**Abstract:**

**Keywords:**
Digital Filters,
Analog Filters,
frequency transformation,
bilinear z-transformation,
pre-warping frequency,
Pascal’s
triangle

##### 22 An Iterative Method for the Symmetric Arrowhead Solution of Matrix Equation

**Authors:**
Minghui Wang,
Luping Xu,
Juntao Zhang

**Abstract:**

**Keywords:**
Iterative Method,
like-minimum norm,
minimum norm,
Symmetric arrowhead matrix,
Algorithm LSQR

##### 21 Solving Linear Matrix Equations by Matrix Decompositions

**Authors:**
Yongxin Yuan,
Kezheng Zuo

**Abstract:**

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

**Keywords:**
generalized inverse,
Matrix Equation,
Generalized
singular-value decomposition

##### 20 A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation

**Authors:**
Minghui Wang,
Juntao Zhang

**Abstract:**

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

**Keywords:**
Convergence,
Inversion-free method,
Hermitian positive definite solution,
Maximal solution

##### 19 On the Positive Definite Solutions of Nonlinear Matrix Equation

**Authors:**
Tian Baoguang,
Liang Chunyan,
Chen Nan

**Abstract:**

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_{i} are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_{i}<0 is proposed.

**Keywords:**
Iterative Method,
Nonlinear matrix equation,
Positive definite solution,
The maximal-minimal solution,
Free-inversion

##### 18 Two Iterative Algorithms to Compute the Bisymmetric Solution of the Matrix Equation A1X1B1 + A2X2B2 + ... + AlXlBl = C

**Authors:**
A.Tajaddini

**Abstract:**

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

**Keywords:**
Bisymmetric matrices,
Paige’s algorithms,
Least
square

##### 17 Algebraic Riccati Matrix Equation for Eigen- Decomposition of Special Structured Matrices; Applications in Structural Mechanics

**Authors:**
Mahdi Nouri

**Abstract:**

In this paper Algebraic Riccati matrix equation is used for Eigen-decomposition of special structured matrices. This is achieved by similarity transformation and then using algebraic riccati matrix equation to triangulation of matrices. The process is decomposition of matrices into small and specially structured submatrices with low dimensions for fast and easy finding of Eigenpairs. Numerical and structural examples included showing the efficiency of present method.

**Keywords:**
Decomposition,
eigenvalue problem,
Matrix Equation,
Graphs theory,
bisymmetric,
Riccati,
symmetric,
persymmetric,
canonical
forms,
adjacency and Laplacian matrices

##### 16 Approximate Solutions to Large Stein Matrix Equations

**Authors:**
Khalide Jbilou

**Abstract:**

In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.

**Keywords:**
journal,
paper,
latex,
template,
IEEEtran

##### 15 Hydrodynamic Modeling of Infinite Reservoir using Finite Element Method

**Authors:**
M. A. Ghorbani,
M. Pasbani Khiavi

**Abstract:**

**Keywords:**
Reservoir,
finite element,
hydrodynamic pressure,
truncated boundary

##### 14 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)

##### 13 A Fast Cyclic Reduction Algorithm for A Quadratic Matrix Equation Arising from Overdamped Systems

**Abstract:**

**Keywords:**
fast algorithm,
Cyclic reduction,
Overdampedquadratic matrix equation,
Structure-preserving doubling algorithm

##### 12 Iterative solutions to the linear matrix equation AXB + CXTD = E

**Authors:**
Yongxin Yuan,
Jiashang Jiang

**Abstract:**

**Keywords:**
Parameter Estimation,
iterative algorithm,
Matrix Equation,
minimum norm solution

##### 11 A Projection Method Based on Extended Krylov Subspaces for Solving Sylvester Equations

**Authors:**
Yiqin Lin,
Liang Bao,
Yimin Wei

**Abstract:**

In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

**Keywords:**
Iterative Method,
krylov subspace,
Arnoldi process,
Sylvester equation,
Dissipative matrix

##### 10 Iterative Solutions to Some Linear Matrix Equations

**Authors:**
Jiashang Jiang,
Hao Liu,
Yongxin Yuan

**Abstract:**

In this paper the gradient based iterative algorithms are presented to solve the following four types linear matrix equations: (a) AXB = F; (b) AXB = F, CXD = G; (c) AXB = F s. t. X = XT ; (d) AXB+CYD = F, where X and Y are unknown matrices, A,B,C,D, F,G are the given constant matrices. It is proved that if the equation considered has a solution, then the unique minimum norm solution can be obtained by choosing a special kind of initial matrices. The numerical results show that the proposed method is reliable and attractive.

**Keywords:**
Parameter Estimation,
iterative algorithm,
Matrix Equation,
minimum norm solution

##### 9 Implicit Two Step Continuous Hybrid Block Methods with Four Off-Steps Points for Solving Stiff Ordinary Differential Equation

**Authors:**
O. A. Akinfenwa,
N.M. Yao,
S. N. Jator

**Abstract:**

**Keywords:**
Stability,
off-step points,
Collocation and Interpolation,
Continuous HybridBlock Formulae,
Stiff ODEs

##### 8 Delay-independent Stabilization of Linear Systems with Multiple Time-delays

**Authors:**
Ping He,
Heng-You Lan,
Gong-Quan Tan

**Abstract:**

**Keywords:**
Linear System,
Delay-independent stabilization,
Lyapunovfunctional,
Riccati algebra matrix equation

##### 7 A Novel System of Two Coupled Equations for the Longitudinal Components of the Electromagnetic Field in a Waveguide

**Authors:**
Arti Vaish,
Harish Parthasarathy

**Abstract:**

**Keywords:**
Electromagnetism,
Maxwell's equations,
Wave Equation,
Anisotropic permittivity,
Matrix Equation,
Permittivity tensor

##### 6 An eighth order Backward Differentiation Formula with Continuous Coefficients for Stiff Ordinary Differential Equations

**Authors:**
Olusheye Akinfenwa,
Samuel Jator,
Nianmin Yoa

**Abstract:**

**Keywords:**
Stability,
Stiff IVPs,
System of ODEs,
Backward differentiationformulas,
Block methods

##### 5 Extending Global Full Orthogonalization method for Solving the Matrix Equation AXB=F

**Authors:**
Fatemeh Panjeh Ali Beik

**Abstract:**

**Keywords:**
Iterative methods,
Matrix equations,
Block Krylovsubspace methods

##### 4 On Positive Definite Solutions of Quaternionic Matrix Equations

**Authors:**
Minghui Wang

**Abstract:**

**Keywords:**
Matrix Equation,
Quaternionic matrix,
Real representation,
positive (semi)definite solutions

##### 3 An Iterative Method for the Least-squares Symmetric Solution of AXB+CYD=F and its Application

**Authors:**
Minghui Wang

**Abstract:**

Based on the classical algorithm LSQR for solving (unconstrained) LS problem, an iterative method is proposed for the least-squares like-minimum-norm symmetric solution of AXB+CYD=E. As the application of this algorithm, an iterative method for the least-squares like-minimum-norm biymmetric solution of AXB=E is also obtained. Numerical results are reported that show the efficiency of the proposed methods.

**Keywords:**
iterative algorithm,
Matrix Equation,
bisymmetric matrix,
least squares problem,
like-minimum norm

##### 2 Algorithms for the Fast Computation of PWL and PHL Transforms

**Authors:**
Fituri H Belgassem,
Abdulbasit Nigrat,
Seddeeq Ghrari

**Abstract:**

In this paper, the construction of fast algorithms for the computation of Periodic Walsh Piecewise-Linear PWL transform and the Periodic Haar Piecewise-Linear PHL transform will be presented. Algorithms for the computation of the inverse transforms are also proposed. The matrix equation of the PWL and PHL transforms are introduced. Comparison of the computational requirements for the periodic piecewise-linear transforms and other orthogonal transforms shows that the periodic piecewise-linear transforms require less number of operations than some orthogonal transforms such as the Fourier, Walsh and the Discrete Cosine transforms.

**Keywords:**
fast algorithms,
Piece wise linear transforms,
Fast transforms

##### 1 Computation of the Filtering Properties of Photonic Crystal Waveguide Discontinuities Using the Mode Matching Method

**Authors:**
Athanasios Theoharidis,
Thomas Kamalakis,
Ioannis Neokosmidis,
Thomas Sphicopoulos

**Abstract:**

**Keywords:**
Optical Communications,
Integrated Optics,
photonic crystals,
Optical Waveguide Discontinuities