scholarly journals Approximating the Matrix Sign Function Using a Novel Iterative Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
F. Soleymani ◽  
P. S. Stanimirović ◽  
S. Shateyi ◽  
F. Khaksar Haghani
Keyword(s):  
Iterative Method ◽  
Asymptotical Stability ◽  
Complex Matrix ◽  
Initial Matrix ◽  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix ◽  
Square Complex

This study presents a matrix iterative method for finding the sign of a square complex matrix. It is shown that the sequence of iterates converges to the sign and has asymptotical stability, provided that the initial matrix is appropriately chosen. Some illustrations are presented to support the theory.

scholarly journals A Novel Iterative Method for Polar Decomposition and Matrix Sign Function

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
F. Soleymani ◽  
Predrag S. Stanimirović ◽  
Igor Stojanović
Keyword(s):  
Computational Complexity ◽  
Iterative Method ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Polar Decomposition ◽  
Matrix Sign Function ◽  
Sign Function ◽  
Globally Convergent ◽  
The Matrix ◽  
Analysis Of Stability

We define and investigate a globally convergent iterative method possessing sixth order of convergence which is intended to calculate the polar decomposition and the matrix sign function. Some analysis of stability and computational complexity are brought forward. The behaviors of the proposed algorithms are illustrated by numerical experiments.

scholarly journals Constructing a High-Order Globally Convergent Iterative Method for Calculating the Matrix Sign Function

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Haifa Bin Jebreen
Keyword(s):  
Iterative Method ◽  
Order Of Convergence ◽  
Eighth Order ◽  
Matrix Sign Function ◽  
Sign Function ◽  
Globally Convergent ◽  
The Matrix ◽  
Matrix Iteration ◽  
Particulate Matrix ◽  
Theoretical Results

This work is concerned with the construction of a new matrix iteration in the form of an iterative method which is globally convergent for finding the sign of a square matrix having no eigenvalues on the axis of imaginary. Toward this goal, a new method is built via an application of a new four-step nonlinear equation solver on a particulate matrix equation. It is discussed that the proposed scheme has global convergence with eighth order of convergence. To illustrate the effectiveness of the theoretical results, several computational experiments are worked out.

The matrix sign function

1995 ◽  
Vol 40 (8) ◽  
pp. 1330-1348 ◽  
Author(s):  
C.S. Kenney ◽  
A.J. Laub
Keyword(s):  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix

An iterative method to solve a nonlinear matrix equation

2016 ◽  
Vol 31 ◽  
pp. 620-632
Author(s):  
Peng Jingjing ◽  
Liao Anping ◽  
Peng Zhenyun
Keyword(s):  
Approximate Solution ◽  
Iterative Method ◽  
Matrix Equation ◽  
Closed Ball ◽  
Open Ball ◽  
Nonlinear Matrix Equation ◽  
Initial Matrix ◽  
Convergence Results ◽  
The Matrix ◽  
Nonlinear Matrix

n this paper, an iterative method to solve one kind of nonlinear matrix equation is discussed. For each initial matrix with some conditions, the matrix sequences generated by the iterative method are shown to lie in a fixed open ball. The matrix sequences generated by the iterative method are shown to converge to the only solution of the nonlinear matrix equation in the fixed closed ball. In addition, the error estimate of the approximate solution in the fixed closed ball, and a numerical example to illustrate the convergence results are given.

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