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.

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.

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

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.

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