Estimation of Large Sparse Systems
In this chapter, the authors introduce decoupled, Jacobi and Gauss-Seidel estimators and develop all the equations necessary for computer implementation. They briefly introduce a hierarchical decomposition scheme and present the corresponding pseudo code algorithm. The authors then proceed to stability analysis of the estimation algorithms proposed. A way to improve the performance of the decoupled estimator is to include the interconnection terms in the optimization procedure at each subsystem level. This leads to an estimation scheme that mimics the well-known Jacobi method for iterative solutions of algebraic equations but is based on entirely different conceptual development. A graph-theoretic hierarchical decomposition scheme has been developed, which is capable of generating the system partitions conducive to the parallel-pipeline estimation processes. The advantage is taken of the special block-triangular structure of the system resulting from the application of a graph-theoretic algorithm. Finally, the authors treat a particular large sparse system example dealing with the estimation of a ship boiler model.