| This dissertation is devoted to the study of development and implementations of parallel algorithms for the Sylvester-observer matrix equation: XA + BX = GC, arising in the construction of Luenberger observer in Control Theory. Though there exist several viable numerical serial algorithms for the problem, no parallel algorithm has been proposed so far.; A new highly parallel algorithm is proposed and implemented on some of the high performance shared-memory and distributed computers of today's choice, such as the CRAY Y-MP, the Siemens S600/10, the Intel iPSC/860, etc. Our experimental results on these machines confirm the efficiency of the algorithm and show that the algorithm is well-suited for achieving high speed on these architectures.; The algorithm and its implementations make use of the state-of-the-art techniques for matrix computations and the recently released LAPACK linear algebra software package.; The new algorithm is compared with a parallel implementation of the best-known sequential method, the Hessenberg-Schur method for the Sylvester equation problem. The study shows the superiority of the proposed algorithm over the Hessenberg-Schur method on parallel architectures.; The research reported in the dissertation will benefit both the applied mathematics and the control engineering communities. |
