Numerical Methods for Very Large Sparse Dynamical Systems

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9405380 Boley This project will develop and experiment with a variety of core numerical algorithms for large sparse or structured linear algebra problems. Part of the research is the development of effective algorithms for the analysis and design of very large control models such as those related to large flexible space structures. To accomplish this, a major focus of this research will be the design of effective and efficient linear algebra algorithms. Examples of problems to be addressed are large Lyapunov equations, large order matrix pencils, large eigenvalue and singular values solvers. Parallel algorithms will be explored and exploited. Approximate solutions obtained via Krylov space methods, or other methods, will be analyzed. A standard sparse matrix library (SPARSKIT) will be used as the foundation for the software development. To evaluate the effectiveness of the algorithms, the quality of controller designs obtained from the approximate solutions will be explored. ***