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

PARALLEL DISTRIBUTED SOLVERS FOR LARGE STABLE GENERALIZED LYAPUNOV EQUATIONS

1999 ◽  
Vol 09 (01) ◽  
pp. 147-158 ◽  
Author(s):  
PETER BENNER ◽  
JOSÉ M. CLAVER ◽  
ENRIQUE S. QUINTANA-ORTI
Keyword(s):  
Large Scale ◽  
Iterative Algorithms ◽  
Direct Methods ◽  
Matrix Equations ◽  
Distributed Architectures ◽  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix ◽  
Qz Algorithm ◽  
Lyapunov Matrix

In this paper we study the solution of stable generalized Lyapunov matrix equations with large-scale, dense coefficient matrices. Our iterative algorithms, based on the matrix sign function, only require scalable matrix algebra kernels which are highly efficient on parallel distributed architectures. This approach avoids therefore the difficult parallelization of direct methods based on the QZ algorithm. The experimental analtsis reports a remarkable performance of our solvers on an IBM SP2 platform.

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