Parallel Solution of Large-Scale Algebraic Bernoulli Equations with the Matrix Sign Function Method

2005 ◽  
Author(s):  
S. Barrachina ◽  
P. Benner ◽  
E.S. Quintana-Orti
Keyword(s):  
Function Method ◽  
Large Scale ◽  
Matrix Sign Function ◽  
Sign Function ◽  
Parallel Solution ◽  
The Matrix

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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