Rational Iterative Methods for the Matrix Sign Function

1991 ◽  
Vol 12 (2) ◽  
pp. 273-291 ◽  
Author(s):  
Charles Kenney ◽  
Alan J. Laub
Keyword(s):  
Iterative Methods ◽  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix

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.

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.

Parallel solution of Riccati matrix equations with the matrix sign function

Automatica ◽  
1998 ◽  
Vol 34 (2) ◽  
pp. 151-156 ◽  
Author(s):  
Enrique S. Quintana-Orti ◽  
Vicente Hernandez
Keyword(s):  
Matrix Equations ◽  
Matrix Sign Function ◽  
Sign Function ◽  
Parallel Solution ◽  
The Matrix ◽  
Riccati Matrix
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