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.

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 Some Matrix Iterations for Computing Matrix Sign Function

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
F. Soleymani ◽  
E. Tohidi ◽  
S. Shateyi ◽  
F. Khaksar Haghani
Keyword(s):  
Convergence Analysis ◽  
Iterative Methods ◽  
Error Bounds ◽  
Numerical Experiments ◽  
Asymptotically Stable ◽  
Stable Convergence ◽  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix

Some iterative methods are introduced and demonstrated for finding the matrix sign function. It is analytically shown that the new schemes are asymptotically stable. Convergence analysis along with the error bounds of the main proposed method is established. Different numerical experiments are employed to compare the behavior of the new schemes with the existing matrix iterations of the same type.

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