A Parallel Algorithm for the Sylvester Observer Equation

Authors:
Christian H. Bischof;Biswa Nath Datta;Avijit Purkayastha
Affiliations:
-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1996

Citing 0
Cited 4

An iterative algorithm for solving a pair of matrix equations AYB=E,CYD=F over generalized centro-symmetric matrices

Computers & Mathematics with Applications
Closed-form solutions to Sylvester-conjugate matrix equations

Computers & Mathematics with Applications
Parallel Solvers for Sylvester-Type Matrix Equations with Applications in Condition Estimation, Part I: Theory and Algorithms

ACM Transactions on Mathematical Software (TOMS)
On solutions of matrix equations V-AVF=BW and V-AVF =BW

Mathematical and Computer Modelling: An International Journal

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Abstract

We present a new algorithm for solving the Sylvester observer equation arising in the context of the Luenberger observer. The algorithm embodies two main computational phases: the solution of several independent equation systems and a series of matrix--matrix multiplications. The algorithm is, thus, well suited for parallel and high-performance computing. By reducing the coefficient matrix $A$ to lower-Hessenberg form, one can implement the algorithm efficiently, with few floating-point operations and little workspace. The algorithm has been successfully implemented on a CRAY C90. A comparison, both theoretical and experimental, has been made with the well-known Hessenberg--Schur algorithm which solves an arbitrary Sylvester equation. Our theoretical analysis and experimental results confirm the superiority of the proposed algorithm, both in efficiency and speed, over the Hessenberg--Schur algorithm.